Szakd
authorAlpar Juttner <alpar@cs.elte.hu>
Tue, 22 Nov 2016 08:15:16 +0100
changeset 220d1b0e5838f
parent 1 76dc74f824ba
child 3 550f81b2f81c
Szakd
Orig/ContactMaps.128.txt
Orig/ContactMaps.16.txt
Orig/ContactMaps.256.txt
Orig/ContactMaps.32.txt
Orig/ContactMaps.64.txt
Orig/ContactMaps.8.txt
Orig/ContactMaps.txt
Orig/Molecules.16.txt
Orig/Molecules.32.txt
Orig/Molecules.64.txt
Orig/Molecules.8.txt
Orig/Molecules.txt
Orig/Proteins.128.txt
Orig/Proteins.16.txt
Orig/Proteins.256.txt
Orig/Proteins.32.txt
Orig/Proteins.64.txt
Orig/Proteins.8.txt
Orig/Proteins.txt
Orig/contactMapIso.txt
Orig/contactMapsIso.txt
Orig/moleculeIso.txt
Orig/moleculesIso.txt
Orig/proteinIso.txt
Orig/proteinsIso.txt
VF2PP/ContactMaps.128.txt
VF2PP/ContactMaps.16.txt
VF2PP/ContactMaps.256.txt
VF2PP/ContactMaps.32.txt
VF2PP/ContactMaps.64.txt
VF2PP/ContactMaps.8.txt
VF2PP/Molecules.16.txt
VF2PP/Molecules.32.txt
VF2PP/Molecules.64.txt
VF2PP/Molecules.8.txt
VF2PP/Proteins.128.txt
VF2PP/Proteins.16.txt
VF2PP/Proteins.256.txt
VF2PP/Proteins.32.txt
VF2PP/Proteins.64.txt
VF2PP/Proteins.8.txt
VF2PPLabel/ContactMaps.128.txt
VF2PPLabel/ContactMaps.16.txt
VF2PPLabel/ContactMaps.256.txt
VF2PPLabel/ContactMaps.32.txt
VF2PPLabel/ContactMaps.64.txt
VF2PPLabel/ContactMaps.8.txt
VF2PPLabel/ContactMaps.txt
VF2PPLabel/Molecules.16.txt
VF2PPLabel/Molecules.32.txt
VF2PPLabel/Molecules.64.txt
VF2PPLabel/Molecules.8.txt
VF2PPLabel/Molecules.txt
VF2PPLabel/Proteins.128.txt
VF2PPLabel/Proteins.16.txt
VF2PPLabel/Proteins.256.txt
VF2PPLabel/Proteins.32.txt
VF2PPLabel/Proteins.64.txt
VF2PPLabel/Proteins.8.txt
VF2PPLabel/Proteins.txt
VF2PPLabel/contactMapIso.txt
VF2PPLabel/contactMapsIso.txt
VF2PPLabel/moleculeIso.txt
VF2PPLabel/moleculesIso.txt
VF2PPLabel/proteinIso.txt
VF2PPLabel/proteinsIso.txt
bibliography.bib
damecco.tex
proteins.txt
proteinsBfs.txt
proteinsOrig.txt
proteinsOrigDeg.txt
randGraph/ind/vf2pInd10_0.05.txt
randGraph/ind/vf2pInd10_0.1.txt
randGraph/ind/vf2pInd10_0.3.txt
randGraph/ind/vf2pInd10_0.6.txt
randGraph/ind/vf2pInd10_0.8.txt
randGraph/ind/vf2pInd10_0.95.txt
randGraph/ind/vf2pInd15_0.05.txt
randGraph/ind/vf2pInd15_0.1.txt
randGraph/ind/vf2pInd15_0.2.txt
randGraph/ind/vf2pInd15_0.3.txt
randGraph/ind/vf2pInd15_0.4.txt
randGraph/ind/vf2pInd15_0.5.txt
randGraph/ind/vf2pInd15_0.6.txt
randGraph/ind/vf2pInd15_0.7.txt
randGraph/ind/vf2pInd15_0.8.txt
randGraph/ind/vf2pInd15_0.95.txt
randGraph/ind/vf2pInd32_0.05.txt
randGraph/ind/vf2pInd32_0.1.txt
randGraph/ind/vf2pInd32_0.3.txt
randGraph/ind/vf2pInd32_0.6.txt
randGraph/ind/vf2pInd32_0.8.txt
randGraph/ind/vf2pInd32_0.95.txt
randGraph/ind/vf2pInd35_0.05.txt
randGraph/ind/vf2pInd35_0.1.txt
randGraph/ind/vf2pInd35_0.3.txt
randGraph/ind/vf2pInd35_0.6.txt
randGraph/ind/vf2pInd35_0.8.txt
randGraph/ind/vf2pInd35_0.95.txt
randGraph/ind/vf2pInd5_0.05.txt
randGraph/ind/vf2pInd5_0.1.txt
randGraph/ind/vf2pInd5_0.3.txt
randGraph/ind/vf2pInd5_0.6.txt
randGraph/ind/vf2pInd5_0.8.txt
randGraph/ind/vf2pInd5_0.95.txt
randGraph/ind/vf2pInd7_0.05.txt
randGraph/ind/vf2pInd7_0.1.txt
randGraph/ind/vf2pInd7_0.3.txt
randGraph/ind/vf2pInd7_0.6.txt
randGraph/ind/vf2pInd7_0.8.txt
randGraph/ind/vf2pInd7_0.95.txt
randGraph/ind/vf2ppInd10_0.05.txt
randGraph/ind/vf2ppInd10_0.1.txt
randGraph/ind/vf2ppInd10_0.3.txt
randGraph/ind/vf2ppInd10_0.6.txt
randGraph/ind/vf2ppInd10_0.8.txt
randGraph/ind/vf2ppInd10_0.95.txt
randGraph/ind/vf2ppInd15_0.05.txt
randGraph/ind/vf2ppInd15_0.1.txt
randGraph/ind/vf2ppInd15_0.2.txt
randGraph/ind/vf2ppInd15_0.3.txt
randGraph/ind/vf2ppInd15_0.4.txt
randGraph/ind/vf2ppInd15_0.5.txt
randGraph/ind/vf2ppInd15_0.6.txt
randGraph/ind/vf2ppInd15_0.7.txt
randGraph/ind/vf2ppInd15_0.8.txt
randGraph/ind/vf2ppInd15_0.95.txt
randGraph/ind/vf2ppInd32_0.05.txt
randGraph/ind/vf2ppInd32_0.1.txt
randGraph/ind/vf2ppInd32_0.3.txt
randGraph/ind/vf2ppInd32_0.6.txt
randGraph/ind/vf2ppInd32_0.8.txt
randGraph/ind/vf2ppInd32_0.95.txt
randGraph/ind/vf2ppInd35_0.05.txt
randGraph/ind/vf2ppInd35_0.1.txt
randGraph/ind/vf2ppInd35_0.3.txt
randGraph/ind/vf2ppInd35_0.6.txt
randGraph/ind/vf2ppInd35_0.8.txt
randGraph/ind/vf2ppInd35_0.95.txt
randGraph/ind/vf2ppInd5_0.05.txt
randGraph/ind/vf2ppInd5_0.1.txt
randGraph/ind/vf2ppInd5_0.3.txt
randGraph/ind/vf2ppInd5_0.6.txt
randGraph/ind/vf2ppInd5_0.8.txt
randGraph/ind/vf2ppInd5_0.95.txt
randGraph/ind/vf2ppInd7_0.05.txt
randGraph/ind/vf2ppInd7_0.1.txt
randGraph/ind/vf2ppInd7_0.3.txt
randGraph/ind/vf2ppInd7_0.6.txt
randGraph/ind/vf2ppInd7_0.8.txt
randGraph/ind/vf2ppInd7_0.95.txt
randGraph/iso/vf2pIso.txt
randGraph/iso/vf2pIso100_1.txt
randGraph/iso/vf2pIso10_1.txt
randGraph/iso/vf2pIso15_1.txt
randGraph/iso/vf2pIso30_1.txt
randGraph/iso/vf2pIso35_1.txt
randGraph/iso/vf2pIso45_1.txt
randGraph/iso/vf2pIso5_1.txt
randGraph/iso/vf2pIso7_1.txt
randGraph/iso/vf2pIso80_1.txt
randGraph/iso/vf2ppIso.txt
randGraph/iso/vf2ppIso100_1.txt
randGraph/iso/vf2ppIso10_1.txt
randGraph/iso/vf2ppIso15_1.txt
randGraph/iso/vf2ppIso30_1.txt
randGraph/iso/vf2ppIso35_1.txt
randGraph/iso/vf2ppIso45_1.txt
randGraph/iso/vf2ppIso5_1.txt
randGraph/iso/vf2ppIso7_1.txt
randGraph/iso/vf2ppIso80_1.txt
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/Orig/ContactMaps.128.txt	Tue Nov 22 08:15:16 2016 +0100
     1.3 @@ -0,0 +1,78 @@
     1.4 +130	0.22081
     1.5 +133	0.206133
     1.6 +136	0.18355
     1.7 +137	0.197773
     1.8 +138	0.196558
     1.9 +140	0.184796
    1.10 +141	0.19825
    1.11 +144	0.18353
    1.12 +146	0.18265
    1.13 +147	0.18449
    1.14 +149	0.18397
    1.15 +150	0.22288
    1.16 +151	0.184963
    1.17 +156	0.18344
    1.18 +157	0.186225
    1.19 +158	0.20248
    1.20 +159	0.18381
    1.21 +162	0.187918
    1.22 +164	0.18324
    1.23 +169	0.18427
    1.24 +181	0.184675
    1.25 +185	0.18532
    1.26 +186	0.18603
    1.27 +187	0.1841
    1.28 +190	0.186097
    1.29 +191	0.18738
    1.30 +192	0.18724
    1.31 +193	0.18642
    1.32 +197	0.18551
    1.33 +198	0.19429
    1.34 +199	0.187057
    1.35 +214	0.18603
    1.36 +220	0.18604
    1.37 +221	0.185745
    1.38 +222	0.18729
    1.39 +224	0.1858
    1.40 +225	0.18676
    1.41 +226	0.20219
    1.42 +228	0.18847
    1.43 +237	0.18467
    1.44 +252	0.18718
    1.45 +264	0.18538
    1.46 +265	0.18966
    1.47 +271	0.185115
    1.48 +274	0.18824
    1.49 +275	0.18339
    1.50 +276	0.20007
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    1.52 +280	0.18887
    1.53 +286	0.19032
    1.54 +302	0.18946
    1.55 +327	0.19141
    1.56 +330	0.18853
    1.57 +334	0.23576
    1.58 +336	0.18842
    1.59 +359	0.19047
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    1.61 +385	0.190206
    1.62 +387	0.189405
    1.63 +388	0.1896
    1.64 +393	0.187709
    1.65 +395	0.18797
    1.66 +414	0.19822
    1.67 +428	0.19766
    1.68 +457	0.189372
    1.69 +484	0.1952
    1.70 +501	0.192085
    1.71 +556	0.18997
    1.72 +558	0.18991
    1.73 +564	0.19406
    1.74 +585	0.18791
    1.75 +599	0.19067
    1.76 +600	0.18935
    1.77 +611	0.19634
    1.78 +617	0.19954
    1.79 +694	0.19411
    1.80 +741	0.19621
    1.81 +773	0.19096
     2.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     2.2 +++ b/Orig/ContactMaps.16.txt	Tue Nov 22 08:15:16 2016 +0100
     2.3 @@ -0,0 +1,90 @@
     2.4 +99	0.019855
     2.5 +102	0.0161067
     2.6 +104	0.0234229
     2.7 +105	0.012285
     2.8 +107	0.01945
     2.9 +114	0.01203
    2.10 +117	0.01158
    2.11 +120	0.0167
    2.12 +122	0.0143667
    2.13 +123	0.02049
    2.14 +124	0.01222
    2.15 +125	0.01525
    2.16 +130	0.01528
    2.17 +133	0.01956
    2.18 +136	0.01626
    2.19 +137	0.0173667
    2.20 +138	0.0182633
    2.21 +140	0.016302
    2.22 +141	0.013885
    2.23 +144	0.01569
    2.24 +146	0.01054
    2.25 +147	0.01312
    2.26 +149	0.01247
    2.27 +150	0.0148
    2.28 +151	0.0217333
    2.29 +156	0.01391
    2.30 +157	0.01783
    2.31 +158	0.016245
    2.32 +159	0.01609
    2.33 +162	0.0180867
    2.34 +164	0.01306
    2.35 +169	0.01068
    2.36 +181	0.015505
    2.37 +185	0.01677
    2.38 +186	0.01562
    2.39 +187	0.02486
    2.40 +190	0.0163967
    2.41 +191	0.01492
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    2.43 +193	0.01498
    2.44 +197	0.01376
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    2.46 +199	0.0155067
    2.47 +214	0.02072
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    2.50 +222	0.024455
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    2.53 +226	0.02636
    2.54 +228	0.03125
    2.55 +237	0.01553
    2.56 +252	0.0317
    2.57 +264	0.03549
    2.58 +265	0.0232
    2.59 +271	0.032805
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    2.62 +276	0.03332
    2.63 +277	0.031835
    2.64 +280	0.0388
    2.65 +286	0.03981
    2.66 +302	0.07635
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    2.69 +334	0.03443
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    2.71 +359	0.03241
    2.72 +360	0.04064
    2.73 +385	0.037878
    2.74 +387	0.039695
    2.75 +388	0.038305
    2.76 +393	0.0378657
    2.77 +395	0.03749
    2.78 +414	0.03428
    2.79 +428	0.04059
    2.80 +457	0.077568
    2.81 +484	0.04291
    2.82 +501	0.05164
    2.83 +556	0.04768
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    2.85 +564	0.05769
    2.86 +585	0.04488
    2.87 +599	0.04262
    2.88 +600	0.05537
    2.89 +611	0.0737
    2.90 +617	0.09413
    2.91 +694	0.05558
    2.92 +741	0.04833
    2.93 +773	0.03812
     3.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     3.2 +++ b/Orig/ContactMaps.256.txt	Tue Nov 22 08:15:16 2016 +0100
     3.3 @@ -0,0 +1,37 @@
     3.4 +264	0.59794
     3.5 +265	0.48155
     3.6 +271	0.449
     3.7 +274	0.5971
     3.8 +275	0.62311
     3.9 +276	0.54627
    3.10 +277	0.551835
    3.11 +280	0.45184
    3.12 +286	0.46273
    3.13 +302	0.49371
    3.14 +327	0.4618
    3.15 +330	0.45889
    3.16 +334	0.49278
    3.17 +336	0.45375
    3.18 +359	0.46987
    3.19 +360	0.47958
    3.20 +385	0.458656
    3.21 +387	0.45593
    3.22 +388	0.475715
    3.23 +393	0.457603
    3.24 +395	0.45579
    3.25 +414	0.48986
    3.26 +428	0.46349
    3.27 +457	0.469788
    3.28 +484	0.46116
    3.29 +501	0.46355
    3.30 +556	0.45775
    3.31 +558	0.44757
    3.32 +564	0.47985
    3.33 +585	0.4657
    3.34 +599	0.45661
    3.35 +600	0.46745
    3.36 +611	0.47708
    3.37 +617	0.49836
    3.38 +694	0.48761
    3.39 +741	0.47429
    3.40 +773	0.48868
     4.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     4.2 +++ b/Orig/ContactMaps.32.txt	Tue Nov 22 08:15:16 2016 +0100
     4.3 @@ -0,0 +1,90 @@
     4.4 +99	0.03134
     4.5 +102	0.02698
     4.6 +104	0.0273114
     4.7 +105	0.022745
     4.8 +107	0.03374
     4.9 +114	0.02345
    4.10 +117	0.0228
    4.11 +120	0.023015
    4.12 +122	0.0263133
    4.13 +123	0.02416
    4.14 +124	0.02359
    4.15 +125	0.03179
    4.16 +130	0.02419
    4.17 +133	0.0248467
    4.18 +136	0.02319
    4.19 +137	0.0269733
    4.20 +138	0.0287983
    4.21 +140	0.026818
    4.22 +141	0.02352
    4.23 +144	0.02264
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    4.25 +147	0.0251
    4.26 +149	0.0244
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    4.28 +151	0.02341
    4.29 +156	0.02408
    4.30 +157	0.02464
    4.31 +158	0.02735
    4.32 +159	0.02316
    4.33 +162	0.02429
    4.34 +164	0.02395
    4.35 +169	0.02329
    4.36 +181	0.02471
    4.37 +185	0.0256
    4.38 +186	0.02635
    4.39 +187	0.02583
    4.40 +190	0.0268067
    4.41 +191	0.02687
    4.42 +192	0.0274
    4.43 +193	0.02694
    4.44 +197	0.02328
    4.45 +198	0.02335
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    4.47 +214	0.0286
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    4.53 +226	0.02814
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    4.56 +252	0.02714
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    4.66 +302	0.03549
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    4.75 +388	0.03197
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    4.80 +457	0.03302
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    4.84 +558	0.03391
    4.85 +564	0.04559
    4.86 +585	0.03263
    4.87 +599	0.03296
    4.88 +600	0.03322
    4.89 +611	0.04289
    4.90 +617	0.05026
    4.91 +694	0.03919
    4.92 +741	0.04012
    4.93 +773	0.03339
     5.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     5.2 +++ b/Orig/ContactMaps.64.txt	Tue Nov 22 08:15:16 2016 +0100
     5.3 @@ -0,0 +1,90 @@
     5.4 +99	0.06413
     5.5 +102	0.06942
     5.6 +104	0.0717
     5.7 +105	0.071015
     5.8 +107	0.07732
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    5.12 +122	0.06583
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    5.14 +124	0.06389
    5.15 +125	0.06419
    5.16 +130	0.06533
    5.17 +133	0.0644333
    5.18 +136	0.06489
    5.19 +137	0.06522
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    5.21 +140	0.068598
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    5.23 +144	0.06284
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    5.25 +147	0.06415
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    5.27 +150	0.06982
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    5.29 +156	0.06389
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    5.34 +164	0.06373
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    5.37 +185	0.06557
    5.38 +186	0.06613
    5.39 +187	0.06552
    5.40 +190	0.06936
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    5.64 +280	0.0689
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    5.92 +741	0.07769
    5.93 +773	0.07191
     6.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     6.2 +++ b/Orig/ContactMaps.8.txt	Tue Nov 22 08:15:16 2016 +0100
     6.3 @@ -0,0 +1,90 @@
     6.4 +99	1.1e-05
     6.5 +102	1.65e-05
     6.6 +104	1.2e-05
     6.7 +105	1.25e-05
     6.8 +107	2.15e-05
     6.9 +114	1.25e-05
    6.10 +117	1.35e-05
    6.11 +120	0.0001175
    6.12 +122	3.9e-05
    6.13 +123	1.5e-05
    6.14 +124	1.45e-05
    6.15 +125	1.55e-05
    6.16 +130	1.6e-05
    6.17 +133	7.3e-05
    6.18 +136	1.6e-05
    6.19 +137	8.65e-05
    6.20 +138	3e-05
    6.21 +140	1.55e-05
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    6.24 +146	1.45e-05
    6.25 +147	2.45e-05
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    6.28 +151	7.35e-05
    6.29 +156	1.8e-05
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    6.32 +159	1.8e-05
    6.33 +162	1.95e-05
    6.34 +164	6.2e-05
    6.35 +169	2.15e-05
    6.36 +181	4.45e-05
    6.37 +185	5.7e-05
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    6.39 +187	9.1e-05
    6.40 +190	2.25e-05
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    6.43 +193	2.65e-05
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    6.58 +265	5.4e-05
    6.59 +271	3.2e-05
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    6.61 +275	4.65e-05
    6.62 +276	0.000166
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    6.65 +286	5.75e-05
    6.66 +302	4.2e-05
    6.67 +327	7.9e-05
    6.68 +330	3.9e-05
    6.69 +334	5.05e-05
    6.70 +336	7.3e-05
    6.71 +359	8.15e-05
    6.72 +360	4.65e-05
    6.73 +385	6.05e-05
    6.74 +387	6.1e-05
    6.75 +388	0.000126
    6.76 +393	4.55e-05
    6.77 +395	5.1e-05
    6.78 +414	0.0001055
    6.79 +428	7.75e-05
    6.80 +457	7.3e-05
    6.81 +484	7.3e-05
    6.82 +501	0.000163
    6.83 +556	7.85e-05
    6.84 +558	7.35e-05
    6.85 +564	0.0002265
    6.86 +585	7e-05
    6.87 +599	7.15e-05
    6.88 +600	0.0001475
    6.89 +611	0.000126
    6.90 +617	0.000144
    6.91 +694	0.000165
    6.92 +741	0.0001345
    6.93 +773	7.3e-05
     7.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     7.2 +++ b/Orig/ContactMaps.txt	Tue Nov 22 08:15:16 2016 +0100
     7.3 @@ -0,0 +1,90 @@
     7.4 +99	5.34361e-05
     7.5 +102	5.37944e-05
     7.6 +104	5.72603e-05
     7.7 +105	5.08056e-05
     7.8 +107	5.85278e-05
     7.9 +114	4.97778e-05
    7.10 +117	5.03278e-05
    7.11 +120	5.69722e-05
    7.12 +122	5.38111e-05
    7.13 +123	5.88944e-05
    7.14 +124	5.25778e-05
    7.15 +125	5.69556e-05
    7.16 +130	0.000113842
    7.17 +133	0.000112197
    7.18 +136	0.000104983
    7.19 +137	0.000111296
    7.20 +138	0.000113233
    7.21 +140	0.000109111
    7.22 +141	0.000110242
    7.23 +144	0.000106004
    7.24 +146	0.000103967
    7.25 +147	0.000106579
    7.26 +149	0.000107263
    7.27 +150	0.000108846
    7.28 +151	0.000108735
    7.29 +156	0.000108296
    7.30 +157	0.000111154
    7.31 +158	0.000118977
    7.32 +159	0.000112633
    7.33 +162	0.000113525
    7.34 +164	0.000110142
    7.35 +169	0.000111287
    7.36 +181	0.000115817
    7.37 +185	0.000119525
    7.38 +186	0.000119171
    7.39 +187	0.000120792
    7.40 +190	0.000120919
    7.41 +191	0.0001214
    7.42 +192	0.000122258
    7.43 +193	0.000122033
    7.44 +197	0.000119675
    7.45 +198	0.000123142
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    7.47 +214	0.000129204
    7.48 +220	0.000131454
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    7.50 +222	0.000132202
    7.51 +224	0.000132292
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    7.57 +264	0.000281152
    7.58 +265	0.000246087
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    7.68 +330	0.000269307
    7.69 +334	0.000276257
    7.70 +336	0.00027925
    7.71 +359	0.000291737
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    7.74 +387	0.000299035
    7.75 +388	0.00029937
    7.76 +393	0.000297727
    7.77 +395	0.0002969
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    7.84 +558	0.000365067
    7.85 +564	0.000386503
    7.86 +585	0.000374733
    7.87 +599	0.00037959
    7.88 +600	0.000385833
    7.89 +611	0.00041654
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    7.92 +741	0.000466307
    7.93 +773	0.00044286
     8.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     8.2 +++ b/Orig/Molecules.16.txt	Tue Nov 22 08:15:16 2016 +0100
     8.3 @@ -0,0 +1,83 @@
     8.4 +17	0.00598246
     8.5 +18	0.00633118
     8.6 +19	0.00615402
     8.7 +20	0.00641676
     8.8 +21	0.00651908
     8.9 +22	0.00684749
    8.10 +23	0.00685846
    8.11 +24	0.007018
    8.12 +25	0.00716316
    8.13 +26	0.00729213
    8.14 +27	0.00745774
    8.15 +28	0.00772876
    8.16 +29	0.00784202
    8.17 +30	0.00805273
    8.18 +31	0.00842222
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    8.21 +34	0.00949043
    8.22 +35	0.00969127
    8.23 +36	0.010043
    8.24 +37	0.0103157
    8.25 +38	0.0107507
    8.26 +39	0.0106857
    8.27 +40	0.0109116
    8.28 +41	0.0106991
    8.29 +42	0.0118399
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    8.32 +45	0.0123581
    8.33 +46	0.0126685
    8.34 +47	0.0123943
    8.35 +48	0.0131893
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    8.37 +50	0.0127309
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    8.50 +63	0.02005
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    8.86 +99	0.0190667
     9.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     9.2 +++ b/Orig/Molecules.32.txt	Tue Nov 22 08:15:16 2016 +0100
     9.3 @@ -0,0 +1,67 @@
     9.4 +33	0.00967075
     9.5 +34	0.00954023
     9.6 +35	0.0097031
     9.7 +36	0.00971922
     9.8 +37	0.0104818
     9.9 +38	0.0100582
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    9.15 +44	0.0099366
    9.16 +45	0.00996648
    9.17 +46	0.0104871
    9.18 +47	0.0104315
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    9.32 +61	0.0106761
    9.33 +62	0.0108289
    9.34 +63	0.010424
    9.35 +64	0.0105851
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    10.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    10.2 +++ b/Orig/Molecules.64.txt	Tue Nov 22 08:15:16 2016 +0100
    10.3 @@ -0,0 +1,35 @@
    10.4 +65	0.0419733
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   10.10 +71	0.0340333
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   10.13 +74	0.0340264
   10.14 +75	0.0374222
   10.15 +76	0.0372697
   10.16 +77	0.0370636
   10.17 +78	0.0367472
   10.18 +79	0.0379667
   10.19 +80	0.0390786
   10.20 +81	0.04476
   10.21 +82	0.0386952
   10.22 +83	0.04104
   10.23 +84	0.0513278
   10.24 +85	0.0638222
   10.25 +86	0.0395556
   10.26 +87	0.03925
   10.27 +88	0.0399
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   10.29 +90	0.0404944
   10.30 +91	0.0412667
   10.31 +92	0.0432
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   10.33 +94	0.0488
   10.34 +95	0.0416222
   10.35 +96	0.0439133
   10.36 +97	0.0421222
   10.37 +98	0.0440333
   10.38 +99	0.0404
    11.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    11.2 +++ b/Orig/Molecules.8.txt	Tue Nov 22 08:15:16 2016 +0100
    11.3 @@ -0,0 +1,90 @@
    11.4 +10	0.00362222
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   11.13 +19	0.00442644
   11.14 +20	0.00477781
   11.15 +21	0.0049817
   11.16 +22	0.00530661
   11.17 +23	0.00555603
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    12.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    12.2 +++ b/Orig/Molecules.txt	Tue Nov 22 08:15:16 2016 +0100
    12.3 @@ -0,0 +1,90 @@
    12.4 +10	3.42778e-06
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    12.7 +13	3.49697e-06
    12.8 +14	4.1619e-06
    12.9 +15	3.6e-06
   12.10 +16	4.37724e-06
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   12.12 +18	5.33871e-06
   12.13 +19	5.08736e-06
   12.14 +20	5.35466e-06
   12.15 +21	5.50116e-06
   12.16 +22	5.80731e-06
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   12.18 +24	5.93047e-06
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   12.93 +99	2.265e-05
    13.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    13.2 +++ b/Orig/Proteins.128.txt	Tue Nov 22 08:15:16 2016 +0100
    13.3 @@ -0,0 +1,234 @@
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    14.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    14.2 +++ b/Orig/Proteins.16.txt	Tue Nov 22 08:15:16 2016 +0100
    14.3 @@ -0,0 +1,234 @@
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    15.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    15.2 +++ b/Orig/Proteins.256.txt	Tue Nov 22 08:15:16 2016 +0100
    15.3 @@ -0,0 +1,234 @@
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    16.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    16.2 +++ b/Orig/Proteins.32.txt	Tue Nov 22 08:15:16 2016 +0100
    16.3 @@ -0,0 +1,234 @@
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    17.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    17.2 +++ b/Orig/Proteins.64.txt	Tue Nov 22 08:15:16 2016 +0100
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    18.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    18.2 +++ b/Orig/Proteins.8.txt	Tue Nov 22 08:15:16 2016 +0100
    18.3 @@ -0,0 +1,234 @@
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    19.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    19.2 +++ b/Orig/Proteins.txt	Tue Nov 22 08:15:16 2016 +0100
    19.3 @@ -0,0 +1,234 @@
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    20.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    20.2 +++ b/Orig/contactMapIso.txt	Tue Nov 22 08:15:16 2016 +0100
    20.3 @@ -0,0 +1,90 @@
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   20.60 +274	1.538
   20.61 +275	1.623
   20.62 +276	1.503
   20.63 +277	1.471
   20.64 +280	1.601
   20.65 +286	1.612
   20.66 +302	1.696
   20.67 +327	1.783
   20.68 +330	1.761
   20.69 +334	1.964
   20.70 +336	1.839
   20.71 +359	2.097
   20.72 +360	2.163
   20.73 +385	2.117
   20.74 +387	2.149
   20.75 +388	2.147
   20.76 +393	2.207
   20.77 +395	2.236
   20.78 +414	2.352
   20.79 +428	2.666
   20.80 +457	2.834
   20.81 +484	3.249
   20.82 +501	3.035
   20.83 +556	3.407
   20.84 +558	3.247
   20.85 +564	3.737
   20.86 +585	3.696
   20.87 +599	3.857
   20.88 +600	3.735
   20.89 +611	4.12
   20.90 +617	3.811
   20.91 +694	5.391
   20.92 +741	5.231
   20.93 +773	4.201
    21.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    21.2 +++ b/Orig/contactMapsIso.txt	Tue Nov 22 08:15:16 2016 +0100
    21.3 @@ -0,0 +1,90 @@
    21.4 +99	0.0349
    21.5 +102	0.0387
    21.6 +104	0.0437
    21.7 +105	0.0424
    21.8 +107	0.0397
    21.9 +114	0.0371
   21.10 +117	0.0419
   21.11 +120	0.0477
   21.12 +122	0.0503
   21.13 +123	0.0481
   21.14 +124	0.0421
   21.15 +125	0.0557
   21.16 +130	0.0559
   21.17 +133	0.0572
   21.18 +136	0.0588
   21.19 +137	0.0589
   21.20 +138	0.058
   21.21 +140	0.0656
   21.22 +141	0.061
   21.23 +144	0.0596
   21.24 +146	0.0335
   21.25 +147	0.0552
   21.26 +149	0.0484
   21.27 +150	0.0605
   21.28 +151	0.0592
   21.29 +156	0.0686
   21.30 +157	0.0706
   21.31 +158	0.0682
   21.32 +159	0.0659
   21.33 +162	0.0685
   21.34 +164	0.0631
   21.35 +169	0.072
   21.36 +181	0.0707
   21.37 +185	0.0855
   21.38 +186	0.0838
   21.39 +187	0.08
   21.40 +190	0.0877
   21.41 +191	0.0872
   21.42 +192	0.0889
   21.43 +193	0.093
   21.44 +197	0.0924
   21.45 +198	0.1006
   21.46 +199	0.0912
   21.47 +214	0.0904
   21.48 +220	0.1014
   21.49 +221	0.1003
   21.50 +222	0.1043
   21.51 +224	0.1029
   21.52 +225	0.1053
   21.53 +226	0.1076
   21.54 +228	0.1089
   21.55 +237	0.1136
   21.56 +252	0.1203
   21.57 +264	0.1302
   21.58 +265	0.124
   21.59 +271	0.1305
   21.60 +274	0.1437
   21.61 +275	0.1494
   21.62 +276	0.1395
   21.63 +277	0.1375
   21.64 +280	0.141
   21.65 +286	0.1408
   21.66 +302	0.1566
   21.67 +327	0.1652
   21.68 +330	0.1653
   21.69 +334	0.1811
   21.70 +336	0.1721
   21.71 +359	0.194
   21.72 +360	0.2031
   21.73 +385	0.1981
   21.74 +387	0.2019
   21.75 +388	0.1988
   21.76 +393	0.2099
   21.77 +395	0.2083
   21.78 +414	0.2197
   21.79 +428	0.2437
   21.80 +457	0.2567
   21.81 +484	0.2966
   21.82 +501	0.2779
   21.83 +556	0.3125
   21.84 +558	0.3062
   21.85 +564	0.3498
   21.86 +585	0.3466
   21.87 +599	0.3545
   21.88 +600	0.3504
   21.89 +611	0.3838
   21.90 +617	0.3602
   21.91 +694	0.5001
   21.92 +741	0.4809
   21.93 +773	0.4004
    22.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    22.2 +++ b/Orig/moleculeIso.txt	Tue Nov 22 08:15:16 2016 +0100
    22.3 @@ -0,0 +1,91 @@
    22.4 +8	0.009
    22.5 +10	0.009
    22.6 +11	0.014
    22.7 +12	0.014
    22.8 +13	0.011
    22.9 +14	0.015
   22.10 +15	0.013
   22.11 +16	0.012
   22.12 +17	0.016
   22.13 +18	0.013
   22.14 +19	0.01
   22.15 +20	0.015
   22.16 +21	0.018
   22.17 +22	0.016
   22.18 +23	0.018
   22.19 +24	0.016
   22.20 +25	0.023
   22.21 +26	0.024
   22.22 +27	0.023
   22.23 +28	0.022
   22.24 +29	0.023
   22.25 +30	0.024
   22.26 +31	0.025
   22.27 +32	0.026
   22.28 +33	0.026
   22.29 +34	0.03
   22.30 +35	0.03
   22.31 +36	0.03
   22.32 +37	0.031
   22.33 +38	0.032
   22.34 +39	0.03
   22.35 +40	0.03
   22.36 +41	0.034
   22.37 +42	0.039
   22.38 +43	0.032
   22.39 +44	0.037
   22.40 +45	0.031
   22.41 +46	0.038
   22.42 +47	0.035
   22.43 +48	0.039
   22.44 +49	0.04
   22.45 +50	0.042
   22.46 +51	0.041
   22.47 +52	0.048
   22.48 +53	0.04
   22.49 +54	0.04
   22.50 +55	0.046
   22.51 +56	0.037
   22.52 +57	0.04
   22.53 +58	0.055
   22.54 +59	0.047
   22.55 +60	0.045
   22.56 +61	0.051
   22.57 +62	0.053
   22.58 +63	0.066
   22.59 +64	0.043
   22.60 +65	0.066
   22.61 +66	0.066
   22.62 +67	0.065
   22.63 +68	0.074
   22.64 +69	0.059
   22.65 +70	0.055
   22.66 +71	0.083
   22.67 +72	0.057
   22.68 +73	0.06
   22.69 +74	0.054
   22.70 +75	0.054
   22.71 +76	0.062
   22.72 +77	0.064
   22.73 +78	0.071
   22.74 +79	0.062
   22.75 +80	0.075
   22.76 +81	0.069
   22.77 +82	0.07
   22.78 +83	0.07
   22.79 +84	0.069
   22.80 +85	0.073
   22.81 +86	0.086
   22.82 +87	0.092
   22.83 +88	0.085
   22.84 +89	0.082
   22.85 +90	0.097
   22.86 +91	0.083
   22.87 +92	0.111
   22.88 +93	0.073
   22.89 +94	0.124
   22.90 +95	0.087
   22.91 +96	0.097
   22.92 +97	0.087
   22.93 +98	0.088
   22.94 +99	0.112
    23.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    23.2 +++ b/Orig/moleculesIso.txt	Tue Nov 22 08:15:16 2016 +0100
    23.3 @@ -0,0 +1,89 @@
    23.4 +8	0.00214
    23.5 +10	0.00289
    23.6 +11	0.00354
    23.7 +12	0.00469
    23.8 +13	0.00355
    23.9 +14	0.00412
   23.10 +15	0.00449
   23.11 +16	0.00418
   23.12 +17	0.00585
   23.13 +18	0.00507
   23.14 +19	0.00426
   23.15 +20	0.00666
   23.16 +21	0.00682
   23.17 +22	0.00644
   23.18 +23	0.00785
   23.19 +24	0.00687
   23.20 +25	0.01061
   23.21 +26	0.00831
   23.22 +27	0.00838
   23.23 +28	0.01307
   23.24 +29	0.0105
   23.25 +30	0.01221
   23.26 +31	0.01033
   23.27 +32	0.01276
   23.28 +33	0.01496
   23.29 +34	0.01311
   23.30 +35	0.01318
   23.31 +36	0.01419
   23.32 +37	0.01445
   23.33 +38	0.01471
   23.34 +39	0.01562
   23.35 +40	0.01423
   23.36 +41	0.01704
   23.37 +42	0.01971
   23.38 +43	0.01602
   23.39 +44	0.02022
   23.40 +45	0.01618
   23.41 +46	0.02056
   23.42 +47	0.01739
   23.43 +48	0.01871
   23.44 +49	0.01775
   23.45 +50	0.01764
   23.46 +51	0.01992
   23.47 +52	0.01969
   23.48 +53	0.01888
   23.49 +54	0.01948
   23.50 +55	0.02089
   23.51 +56	0.01696
   23.52 +57	0.01885
   23.53 +58	0.02133
   23.54 +59	0.02238
   23.55 +60	0.0212
   23.56 +61	0.02596
   23.57 +62	0.02761
   23.58 +63	0.02743
   23.59 +64	0.02153
   23.60 +65	0.02993
   23.61 +66	0.03349
   23.62 +67	0.0314
   23.63 +68	0.0351
   23.64 +69	0.0246
   23.65 +70	0.02679
   23.66 +71	0.03377
   23.67 +72	0.0278
   23.68 +73	0.02835
   23.69 +74	0.02895
   23.70 +75	0.02715
   23.71 +76	0.03037
   23.72 +77	0.03238
   23.73 +78	0.03211
   23.74 +79	0.03462
   23.75 +80	0.03723
   23.76 +81	0.03793
   23.77 +82	0.03227
   23.78 +83	0.03539
   23.79 +84	0.03406
   23.80 +85	0.03441
   23.81 +86	0.04042
   23.82 +87	0.03769
   23.83 +88	0.03697
   23.84 +89	0.04212
   23.85 +91	0.03941
   23.86 +93	0.04149
   23.87 +94	0.04669
   23.88 +95	0.04263
   23.89 +96	0.04419
   23.90 +97	0.04054
   23.91 +98	0.04179
   23.92 +99	0.04812
    24.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    24.2 +++ b/Orig/proteinIso.txt	Tue Nov 22 08:15:16 2016 +0100
    24.3 @@ -0,0 +1,234 @@
    24.4 +535	1.069
    24.5 +554	1.143
    24.6 +571	1.299
    24.7 +614	1.331
    24.8 +634	1.439
    24.9 +636	1.477
   24.10 +639	1.451
   24.11 +730	1.87
   24.12 +731	1.903
   24.13 +734	2.025
   24.14 +735	1.897
   24.15 +737	1.938
   24.16 +755	1.982
   24.17 +760	2.175
   24.18 +788	2.207
   24.19 +794	2.373
   24.20 +795	2.183
   24.21 +802	2.206
   24.22 +816	2.268
   24.23 +819	2.419
   24.24 +831	2.409
   24.25 +833	2.432
   24.26 +838	2.376
   24.27 +858	2.511
   24.28 +861	2.592
   24.29 +874	2.581
   24.30 +877	2.585
   24.31 +879	2.609
   24.32 +886	2.851
   24.33 +899	2.731
   24.34 +957	3.039
   24.35 +982	3.273
   24.36 +995	3.267
   24.37 +1019	3.489
   24.38 +1022	3.462
   24.39 +1046	3.622
   24.40 +1049	3.629
   24.41 +1060	3.837
   24.42 +1073	3.861
   24.43 +1076	3.853
   24.44 +1097	4.068
   24.45 +1140	4.22
   24.46 +1156	4.367
   24.47 +1183	4.528
   24.48 +1192	4.608
   24.49 +1202	5.595
   24.50 +1227	4.938
   24.51 +1271	5.279
   24.52 +1300	5.488
   24.53 +1304	5.437
   24.54 +1312	5.72
   24.55 +1356	5.976
   24.56 +1494	7.134
   24.57 +1502	8.15
   24.58 +1559	7.822
   24.59 +1568	7.824
   24.60 +1576	8.457
   24.61 +1605	8.123
   24.62 +1608	8.801
   24.63 +1625	8.968
   24.64 +1632	9.29
   24.65 +1635	9.113
   24.66 +1648	9.986
   24.67 +1674	8.959
   24.68 +1684	9.119
   24.69 +1732	9.504
   24.70 +1744	10.306
   24.71 +1750	9.97
   24.72 +1754	11.228
   24.73 +1764	10.573
   24.74 +1775	10.007
   24.75 +1826	10.534
   24.76 +1844	11.526
   24.77 +1886	11.179
   24.78 +1930	11.844
   24.79 +1938	11.87
   24.80 +1948	11.886
   24.81 +1995	12.518
   24.82 +2000	13.394
   24.83 +2020	12.788
   24.84 +2044	13.162
   24.85 +2086	14.446
   24.86 +2115	14.052
   24.87 +2123	14.273
   24.88 +2126	14.565
   24.89 +2138	14.486
   24.90 +2168	14.635
   24.91 +2190	14.84
   24.92 +2222	15.311
   24.93 +2250	15.622
   24.94 +2298	16.504
   24.95 +2314	16.704
   24.96 +2316	16.47
   24.97 +2325	18.018
   24.98 +2327	16.582
   24.99 +2329	16.898
  24.100 +2344	17.201
  24.101 +2348	16.955
  24.102 +2355	17.22
  24.103 +2379	17.399
  24.104 +2383	17.421
  24.105 +2413	17.892
  24.106 +2423	17.98
  24.107 +2464	18.903
  24.108 +2466	18.911
  24.109 +2512	19.285
  24.110 +2546	19.636
  24.111 +2553	20.608
  24.112 +2593	20.407
  24.113 +2604	20.587
  24.114 +2605	22.925
  24.115 +2607	22.02
  24.116 +2610	22.058
  24.117 +2611	20.714
  24.118 +2612	22.399
  24.119 +2613	20.741
  24.120 +2616	20.734
  24.121 +2620	20.816
  24.122 +2622	20.836
  24.123 +2625	23.002
  24.124 +2648	21.074
  24.125 +2651	21.203
  24.126 +2716	22.383
  24.127 +2733	22.638
  24.128 +2775	23.708
  24.129 +2812	24.236
  24.130 +2838	24.318
  24.131 +2857	24.726
  24.132 +2872	24.967
  24.133 +2887	25.232
  24.134 +2916	25.613
  24.135 +2920	25.956
  24.136 +2928	26.125
  24.137 +2949	26.15
  24.138 +2966	26.491
  24.139 +2977	28.792
  24.140 +2991	26.936
  24.141 +3104	29.15
  24.142 +3130	29.567
  24.143 +3131	29.599
  24.144 +3134	29.537
  24.145 +3135	29.58
  24.146 +3172	32.619
  24.147 +3182	30.799
  24.148 +3209	30.968
  24.149 +3243	31.605
  24.150 +3255	31.917
  24.151 +3310	32.849
  24.152 +3366	37.254
  24.153 +3429	35.516
  24.154 +3459	35.948
  24.155 +3469	36.118
  24.156 +3483	36.311
  24.157 +3497	37.724
  24.158 +3502	36.693
  24.159 +3505	36.826
  24.160 +3515	37.302
  24.161 +3517	37
  24.162 +3522	37.049
  24.163 +3523	37.207
  24.164 +3526	37.279
  24.165 +3529	37.504
  24.166 +3560	37.933
  24.167 +3563	37.97
  24.168 +3566	38.104
  24.169 +3574	41.274
  24.170 +3582	38.911
  24.171 +3584	38.693
  24.172 +3618	42.161
  24.173 +3619	39.329
  24.174 +3623	42.255
  24.175 +3703	41.236
  24.176 +3711	41.072
  24.177 +3819	43.676
  24.178 +3829	43.854
  24.179 +3839	44.288
  24.180 +3870	44.748
  24.181 +3906	45.735
  24.182 +4025	48.558
  24.183 +4083	50.176
  24.184 +4156	52.911
  24.185 +4194	52.261
  24.186 +4220	52.864
  24.187 +4244	57.808
  24.188 +4283	58.769
  24.189 +4353	56.757
  24.190 +4382	56.877
  24.191 +4389	57.042
  24.192 +4421	57.984
  24.193 +4446	59.382
  24.194 +4521	60.846
  24.195 +4531	60.868
  24.196 +4532	60.751
  24.197 +4568	62.485
  24.198 +4573	66.916
  24.199 +4582	62.751
  24.200 +4604	67.785
  24.201 +4629	64.027
  24.202 +4710	66.067
  24.203 +4713	66.413
  24.204 +4797	68.111
  24.205 +4879	70.489
  24.206 +4970	72.896
  24.207 +5059	75.988
  24.208 +5126	77.531
  24.209 +5241	80.788
  24.210 +5254	81.485
  24.211 +5271	82.209
  24.212 +5318	89.984
  24.213 +5346	84.387
  24.214 +5455	87.669
  24.215 +5492	88.66
  24.216 +5608	92.515
  24.217 +5735	97.315
  24.218 +5775	98.216
  24.219 +5777	98.269
  24.220 +5795	99.811
  24.221 +5845	100.942
  24.222 +5859	101.083
  24.223 +5877	101.587
  24.224 +5945	105.329
  24.225 +5974	104.948
  24.226 +5976	104.704
  24.227 +5983	105.662
  24.228 +6261	115.383
  24.229 +6606	128.002
  24.230 +6713	132.525
  24.231 +6778	145.161
  24.232 +6883	138.36
  24.233 +7349	158.714
  24.234 +7453	163.23
  24.235 +9114	242.24
  24.236 +9174	244.585
  24.237 +10081	295.288
    25.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    25.2 +++ b/Orig/proteinsIso.txt	Tue Nov 22 08:15:16 2016 +0100
    25.3 @@ -0,0 +1,234 @@
    25.4 +535	0.1026
    25.5 +554	0.1098
    25.6 +571	0.1199
    25.7 +614	0.131
    25.8 +634	0.1407
    25.9 +636	0.1439
   25.10 +639	0.1433
   25.11 +730	0.1818
   25.12 +731	0.1823
   25.13 +734	0.1857
   25.14 +735	0.1834
   25.15 +737	0.1883
   25.16 +755	0.1935
   25.17 +760	0.1947
   25.18 +788	0.2109
   25.19 +794	0.214
   25.20 +795	0.2146
   25.21 +802	0.2168
   25.22 +816	0.225
   25.23 +819	0.227
   25.24 +831	0.2305
   25.25 +833	0.2311
   25.26 +838	0.2345
   25.27 +858	0.2436
   25.28 +861	0.2476
   25.29 +874	0.2516
   25.30 +877	0.2528
   25.31 +879	0.257
   25.32 +886	0.2598
   25.33 +899	0.2651
   25.34 +957	0.2984
   25.35 +982	0.316
   25.36 +995	0.3251
   25.37 +1019	0.3412
   25.38 +1022	0.3391
   25.39 +1046	0.3555
   25.40 +1049	0.3567
   25.41 +1060	0.3628
   25.42 +1073	0.3769
   25.43 +1076	0.3735
   25.44 +1097	0.3869
   25.45 +1140	0.4171
   25.46 +1156	0.4276
   25.47 +1183	0.4452
   25.48 +1192	0.4535
   25.49 +1202	0.4626
   25.50 +1227	0.4815
   25.51 +1271	0.5108
   25.52 +1300	0.5313
   25.53 +1304	0.5402
   25.54 +1312	0.5451
   25.55 +1356	0.5765
   25.56 +1494	0.7052
   25.57 +1502	0.7017
   25.58 +1559	0.7573
   25.59 +1568	0.7675
   25.60 +1576	0.7678
   25.61 +1605	0.7975
   25.62 +1608	0.8003
   25.63 +1625	0.8217
   25.64 +1632	0.8223
   25.65 +1635	0.8315
   25.66 +1648	0.8444
   25.67 +1674	0.8698
   25.68 +1684	0.8829
   25.69 +1732	0.9302
   25.70 +1744	0.9393
   25.71 +1750	0.9475
   25.72 +1754	0.9523
   25.73 +1764	0.9621
   25.74 +1775	0.9685
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  25.183 +4083	4.9345
  25.184 +4156	5.1423
  25.185 +4194	5.2471
  25.186 +4220	5.2664
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  25.190 +4382	5.6722
  25.191 +4389	5.6938
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  25.195 +4531	6.1282
  25.196 +4532	6.1396
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  25.200 +4604	6.7524
  25.201 +4629	6.3186
  25.202 +4710	6.6035
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  25.204 +4797	6.7719
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  25.206 +4970	7.3502
  25.207 +5059	7.5207
  25.208 +5126	7.7191
  25.209 +5241	8.1483
  25.210 +5254	8.193
  25.211 +5271	8.1534
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  25.214 +5455	8.7377
  25.215 +5492	8.9213
  25.216 +5608	9.2193
  25.217 +5735	9.6252
  25.218 +5775	9.778
  25.219 +5777	9.7835
  25.220 +5795	9.9526
  25.221 +5845	10.1218
  25.222 +5859	10.0552
  25.223 +5877	10.1402
  25.224 +5945	10.3402
  25.225 +5974	10.4502
  25.226 +5976	10.4729
  25.227 +5983	10.4766
  25.228 +6261	11.4647
  25.229 +6606	12.8157
  25.230 +6713	13.1815
  25.231 +6778	13.39
  25.232 +6883	13.8104
  25.233 +7349	15.7639
  25.234 +7453	16.1769
  25.235 +9114	24.0921
  25.236 +9174	24.3965
  25.237 +10081	29.5504
    26.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    26.2 +++ b/VF2PP/ContactMaps.8.txt	Tue Nov 22 08:15:16 2016 +0100
    26.3 @@ -0,0 +1,90 @@
    26.4 +99	3.5e-06
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    27.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    27.2 +++ b/VF2PPLabel/ContactMaps.128.txt	Tue Nov 22 08:15:16 2016 +0100
    27.3 @@ -0,0 +1,78 @@
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   27.15 +150	0.19709
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   27.17 +156	0.18175
   27.18 +157	0.18332
   27.19 +158	0.201365
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   27.27 +187	0.185
   27.28 +190	0.184773
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    28.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    28.2 +++ b/VF2PPLabel/ContactMaps.16.txt	Tue Nov 22 08:15:16 2016 +0100
    28.3 @@ -0,0 +1,90 @@
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    29.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    29.2 +++ b/VF2PPLabel/ContactMaps.256.txt	Tue Nov 22 08:15:16 2016 +0100
    29.3 @@ -0,0 +1,37 @@
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   29.31 +558	0.45866
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   29.34 +599	0.46784
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   29.36 +611	0.47136
   29.37 +617	0.49935
   29.38 +694	0.48924
   29.39 +741	0.46741
   29.40 +773	0.45467
    30.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    30.2 +++ b/VF2PPLabel/ContactMaps.32.txt	Tue Nov 22 08:15:16 2016 +0100
    30.3 @@ -0,0 +1,90 @@
    30.4 +99	0.03069
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   30.40 +190	0.0256967
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    31.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    31.2 +++ b/VF2PPLabel/ContactMaps.64.txt	Tue Nov 22 08:15:16 2016 +0100
    31.3 @@ -0,0 +1,90 @@
    31.4 +99	0.062625
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   31.21 +140	0.06757
   31.22 +141	0.0648283
   31.23 +144	0.062
   31.24 +146	0.06235
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   31.26 +149	0.06357
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   31.28 +151	0.06307
   31.29 +156	0.06283
   31.30 +157	0.065105
   31.31 +158	0.071395
   31.32 +159	0.06262
   31.33 +162	0.0647878
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   31.35 +169	0.06325
   31.36 +181	0.063735
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   31.38 +186	0.06447
   31.39 +187	0.06389
   31.40 +190	0.0682533
   31.41 +191	0.06632
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   31.55 +237	0.06392
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   31.57 +264	0.065955
   31.58 +265	0.06672
   31.59 +271	0.06441
   31.60 +274	0.06778
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   31.62 +276	0.06579
   31.63 +277	0.116865
   31.64 +280	0.0681
   31.65 +286	0.07101
   31.66 +302	0.06874
   31.67 +327	0.07211
   31.68 +330	0.06596
   31.69 +334	0.07703
   31.70 +336	0.07128
   31.71 +359	0.06922
   31.72 +360	0.06718
   31.73 +385	0.070122
   31.74 +387	0.069785
   31.75 +388	0.068935
   31.76 +393	0.0675257
   31.77 +395	0.06648
   31.78 +414	0.07675
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   31.80 +457	0.070744
   31.81 +484	0.07329
   31.82 +501	0.07195
   31.83 +556	0.07002
   31.84 +558	0.06943
   31.85 +564	0.0775
   31.86 +585	0.06635
   31.87 +599	0.06678
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   31.89 +611	0.07515
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   31.91 +694	0.07412
   31.92 +741	0.07583
   31.93 +773	0.07077
    32.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    32.2 +++ b/VF2PPLabel/ContactMaps.8.txt	Tue Nov 22 08:15:16 2016 +0100
    32.3 @@ -0,0 +1,90 @@
    32.4 +99	3.5e-06
    32.5 +102	7.5e-06
    32.6 +104	4e-06
    32.7 +105	4.5e-06
    32.8 +107	1.2e-05
    32.9 +114	4.5e-06
   32.10 +117	4e-06
   32.11 +120	0.000131
   32.12 +122	1.75e-05
   32.13 +123	4e-06
   32.14 +124	5.5e-06
   32.15 +125	4e-06
   32.16 +130	5e-06
   32.17 +133	7e-05
   32.18 +136	4.5e-06
   32.19 +137	7.75e-05
   32.20 +138	1.65e-05
   32.21 +140	4.5e-06
   32.22 +141	5e-06
   32.23 +144	6.5e-06
   32.24 +146	5.5e-06
   32.25 +147	1.55e-05
   32.26 +149	5e-06
   32.27 +150	5.5e-06
   32.28 +151	5.85e-05
   32.29 +156	4.5e-06
   32.30 +157	7.9e-05
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   32.32 +159	4.5e-06
   32.33 +162	5e-06
   32.34 +164	4.7e-05
   32.35 +169	7.5e-06
   32.36 +181	2.55e-05
   32.37 +185	3.95e-05
   32.38 +186	5.4e-05
   32.39 +187	8.1e-05
   32.40 +190	6e-06
   32.41 +191	8.5e-06
   32.42 +192	8.5e-06
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   32.57 +264	6.15e-05
   32.58 +265	2.95e-05
   32.59 +271	6e-06
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   32.62 +276	0.000103
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   32.68 +330	7e-06
   32.69 +334	1.35e-05
   32.70 +336	3.45e-05
   32.71 +359	3.8e-05
   32.72 +360	1e-05
   32.73 +385	2.2e-05
   32.74 +387	2.3e-05
   32.75 +388	4.3e-05
   32.76 +393	8e-06
   32.77 +395	1.3e-05
   32.78 +414	5.5e-05
   32.79 +428	3.75e-05
   32.80 +457	1.75e-05
   32.81 +484	2.2e-05
   32.82 +501	0.0001015
   32.83 +556	2.05e-05
   32.84 +558	1.8e-05
   32.85 +564	0.000184
   32.86 +585	1.05e-05
   32.87 +599	1e-05
   32.88 +600	2.45e-05
   32.89 +611	6e-05
   32.90 +617	7.85e-05
   32.91 +694	4.25e-05
   32.92 +741	5.15e-05
   32.93 +773	1.25e-05
    33.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    33.2 +++ b/VF2PPLabel/ContactMaps.txt	Tue Nov 22 08:15:16 2016 +0100
    33.3 @@ -0,0 +1,90 @@
    33.4 +99	3.55861e-05
    33.5 +102	3.48204e-05
    33.6 +104	3.82857e-05
    33.7 +105	3.27361e-05
    33.8 +107	4.155e-05
    33.9 +114	2.985e-05
   33.10 +117	2.91611e-05
   33.11 +120	3.40694e-05
   33.12 +122	3.21074e-05
   33.13 +123	3.34333e-05
   33.14 +124	3.04222e-05
   33.15 +125	3.40778e-05
   33.16 +130	7.72042e-05
   33.17 +133	7.44806e-05
   33.18 +136	6.73958e-05
   33.19 +137	7.2275e-05
   33.20 +138	7.38313e-05
   33.21 +140	6.9265e-05
   33.22 +141	7.06243e-05
   33.23 +144	6.62625e-05
   33.24 +146	6.535e-05
   33.25 +147	6.59417e-05
   33.26 +149	6.74542e-05
   33.27 +150	6.75e-05
   33.28 +151	6.84764e-05
   33.29 +156	6.6225e-05
   33.30 +157	6.81729e-05
   33.31 +158	7.44188e-05
   33.32 +159	6.7125e-05
   33.33 +162	6.9319e-05
   33.34 +164	6.64e-05
   33.35 +169	6.52042e-05
   33.36 +181	6.78417e-05
   33.37 +185	6.90083e-05
   33.38 +186	6.86083e-05
   33.39 +187	7.00875e-05
   33.40 +190	6.96403e-05
   33.41 +191	6.99542e-05
   33.42 +192	7.03875e-05
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   33.44 +197	6.64583e-05
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   33.55 +237	6.83292e-05
   33.56 +252	7.39167e-05
   33.57 +264	0.00016664
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   33.59 +271	0.000139285
   33.60 +274	0.000156853
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   33.63 +277	0.000172348
   33.64 +280	0.00014612
   33.65 +286	0.00014713
   33.66 +302	0.000154183
   33.67 +327	0.000143703
   33.68 +330	0.000139873
   33.69 +334	0.00014221
   33.70 +336	0.000143023
   33.71 +359	0.000145047
   33.72 +360	0.00014404
   33.73 +385	0.000144682
   33.74 +387	0.000145017
   33.75 +388	0.00014499
   33.76 +393	0.000143265
   33.77 +395	0.000142503
   33.78 +414	0.000149473
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   33.80 +457	0.000154736
   33.81 +484	0.000152073
   33.82 +501	0.00015102
   33.83 +556	0.00014716
   33.84 +558	0.000145393
   33.85 +564	0.00015671
   33.86 +585	0.000143333
   33.87 +599	0.000143203
   33.88 +600	0.000148243
   33.89 +611	0.000159897
   33.90 +617	0.00016459
   33.91 +694	0.000153237
   33.92 +741	0.000152753
   33.93 +773	0.000145913
    34.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    34.2 +++ b/VF2PPLabel/Molecules.16.txt	Tue Nov 22 08:15:16 2016 +0100
    34.3 @@ -0,0 +1,83 @@
    34.4 +17	0.00495965
    34.5 +18	0.00497957
    34.6 +19	0.00457816
    34.7 +20	0.00490217
    34.8 +21	0.00498796
    34.9 +22	0.00517449
   34.10 +23	0.00517936
   34.11 +24	0.0052692
   34.12 +25	0.00542249
   34.13 +26	0.00539213
   34.14 +27	0.005525
   34.15 +28	0.00576781
   34.16 +29	0.00580222
   34.17 +30	0.00599601
   34.18 +31	0.00625101
   34.19 +32	0.00624525
   34.20 +33	0.00689798
   34.21 +34	0.00697065
   34.22 +35	0.0071004
   34.23 +36	0.00728739
   34.24 +37	0.00760899
   34.25 +38	0.0079363
   34.26 +39	0.00785179
   34.27 +40	0.00806244
   34.28 +41	0.00762517
   34.29 +42	0.00879167
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   34.31 +44	0.00851803
   34.32 +45	0.0095854
   34.33 +46	0.00951061
   34.34 +47	0.00931862
   34.35 +48	0.0100695
   34.36 +49	0.0103389
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   34.38 +51	0.010075
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   34.40 +53	0.0107853
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   34.44 +57	0.00996061
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   34.49 +62	0.026209
   34.50 +63	0.01644
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   34.61 +74	0.0109157
   34.62 +75	0.0103389
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   34.74 +87	0.0125
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   34.77 +90	0.01705
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   34.85 +98	0.0190333
   34.86 +99	0.0121333
    35.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    35.2 +++ b/VF2PPLabel/Molecules.32.txt	Tue Nov 22 08:15:16 2016 +0100
    35.3 @@ -0,0 +1,67 @@
    35.4 +33	0.0088516
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    35.6 +35	0.0089019
    35.7 +36	0.00892661
    35.8 +37	0.00934135
    35.9 +38	0.00913992
   35.10 +39	0.00895817
   35.11 +40	0.00898657
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   35.13 +42	0.00909578
   35.14 +43	0.0090297
   35.15 +44	0.00885774
   35.16 +45	0.00909905
   35.17 +46	0.00958855
   35.18 +47	0.00956703
   35.19 +48	0.00926321
   35.20 +49	0.00936667
   35.21 +50	0.00983
   35.22 +51	0.00912033
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   35.24 +53	0.00911119
   35.25 +54	0.00914
   35.26 +55	0.00945057
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   35.28 +57	0.00904509
   35.29 +58	0.00987424
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   35.32 +61	0.00987214
   35.33 +62	0.00994378
   35.34 +63	0.009666
   35.35 +64	0.00969488
   35.36 +65	0.0093088
   35.37 +66	0.00976769
   35.38 +67	0.01016
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   35.41 +70	0.00960222
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   35.52 +81	0.009868
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   35.54 +83	0.010328
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   35.58 +87	0.00873
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   35.61 +90	0.0109867
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   35.69 +98	0.00932
   35.70 +99	0.01066
    36.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    36.2 +++ b/VF2PPLabel/Molecules.64.txt	Tue Nov 22 08:15:16 2016 +0100
    36.3 @@ -0,0 +1,35 @@
    36.4 +65	0.0229187
    36.5 +66	0.0255346
    36.6 +67	0.0202583
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    36.8 +69	0.0187179
    36.9 +70	0.0182259
   36.10 +71	0.0164714
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   36.13 +74	0.0166088
   36.14 +75	0.0216333
   36.15 +76	0.0173879
   36.16 +77	0.0186
   36.17 +78	0.0186694
   36.18 +79	0.0185061
   36.19 +80	0.019
   36.20 +81	0.0213
   36.21 +82	0.0185095
   36.22 +83	0.0187533
   36.23 +84	0.061625
   36.24 +85	0.104228
   36.25 +86	0.0188444
   36.26 +87	0.01615
   36.27 +88	0.0183444
   36.28 +89	0.0193
   36.29 +90	0.0198111
   36.30 +91	0.0199385
   36.31 +92	0.0230278
   36.32 +93	0.0211917
   36.33 +94	0.0191
   36.34 +95	0.0197222
   36.35 +96	0.02086
   36.36 +97	0.0200278
   36.37 +98	0.0208333
   36.38 +99	0.0178667
    37.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    37.2 +++ b/VF2PPLabel/Molecules.8.txt	Tue Nov 22 08:15:16 2016 +0100
    37.3 @@ -0,0 +1,90 @@
    37.4 +10	0.00294444
    37.5 +11	0.00335333
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    37.7 +13	0.0029697
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   37.11 +17	0.00336491
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   37.13 +19	0.00343103
   37.14 +20	0.00379746
   37.15 +21	0.00401917
   37.16 +22	0.00424404
   37.17 +23	0.00455385
   37.18 +24	0.00430227
   37.19 +25	0.00438118
   37.20 +26	0.0043125
   37.21 +27	0.00477599
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   37.24 +30	0.00476051
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   37.74 +80	0.0098881
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   37.92 +98	0.0229333
   37.93 +99	0.00636667
    38.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    38.2 +++ b/VF2PPLabel/Molecules.txt	Tue Nov 22 08:15:16 2016 +0100
    38.3 @@ -0,0 +1,90 @@
    38.4 +10	2.82778e-06
    38.5 +11	3.2e-06
    38.6 +12	3.12222e-06
    38.7 +13	2.8e-06
    38.8 +14	3.63333e-06
    38.9 +15	3.02778e-06
   38.10 +16	4.1252e-06
   38.11 +17	4.01491e-06
   38.12 +18	4.27312e-06
   38.13 +19	3.82471e-06
   38.14 +20	4.13578e-06
   38.15 +21	4.27413e-06
   38.16 +22	4.46983e-06
   38.17 +23	4.60968e-06
   38.18 +24	4.53713e-06
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   38.23 +29	5.11172e-06
   38.24 +30	5.09723e-06
   38.25 +31	5.25499e-06
   38.26 +32	5.23766e-06
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   38.29 +35	6.33558e-06
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   38.31 +37	6.82543e-06
   38.32 +38	6.9322e-06
   38.33 +39	6.67463e-06
   38.34 +40	6.8121e-06
   38.35 +41	6.51111e-06
   38.36 +42	7.46667e-06
   38.37 +43	7.39511e-06
   38.38 +44	7.33375e-06
   38.39 +45	8.23778e-06
   38.40 +46	7.74192e-06
   38.41 +47	7.97237e-06
   38.42 +48	8.38532e-06
   38.43 +49	8.58086e-06
   38.44 +50	7.54314e-06
   38.45 +51	7.98648e-06
   38.46 +52	8.96193e-06
   38.47 +53	8.9049e-06
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   38.51 +57	8.36222e-06
   38.52 +58	9.06478e-06
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   38.54 +60	1.07001e-05
   38.55 +61	1.44615e-05
   38.56 +62	1.7156e-05
   38.57 +63	1.20858e-05
   38.58 +64	1.03636e-05
   38.59 +65	1.41263e-05
   38.60 +66	1.45346e-05
   38.61 +67	1.22873e-05
   38.62 +68	1.13522e-05
   38.63 +69	1.18887e-05
   38.64 +70	1.17148e-05
   38.65 +71	1.0844e-05
   38.66 +72	1.10975e-05
   38.67 +73	1.17917e-05
   38.68 +74	1.13937e-05
   38.69 +75	1.27069e-05
   38.70 +76	1.21189e-05
   38.71 +77	1.2303e-05
   38.72 +78	1.21819e-05
   38.73 +79	1.21841e-05
   38.74 +80	1.25482e-05
   38.75 +81	1.4385e-05
   38.76 +82	1.42595e-05
   38.77 +83	1.3385e-05
   38.78 +84	2.06333e-05
   38.79 +85	2.97014e-05
   38.80 +86	1.51139e-05
   38.81 +87	1.35042e-05
   38.82 +88	1.485e-05
   38.83 +89	1.3075e-05
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   38.85 +91	1.38647e-05
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   38.91 +97	1.59972e-05
   38.92 +98	1.71917e-05
   38.93 +99	1.14333e-05
    39.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    39.2 +++ b/VF2PPLabel/Proteins.128.txt	Tue Nov 22 08:15:16 2016 +0100
    39.3 @@ -0,0 +1,234 @@
    39.4 +535	0.06442
    39.5 +554	0.0646
    39.6 +571	0.0733
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    39.8 +634	0.07198
    39.9 +636	0.06922
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   39.13 +734	0.10516
   39.14 +735	0.06918
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   39.16 +755	0.07286
   39.17 +760	0.0758
   39.18 +788	0.0883233
   39.19 +794	0.092585
   39.20 +795	0.08052
   39.21 +802	0.0961
   39.22 +816	0.08024
   39.23 +819	0.09148
   39.24 +831	0.08502
   39.25 +833	0.09106
   39.26 +838	0.08378
   39.27 +858	0.07614
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   39.34 +957	0.0901
   39.35 +982	0.09578
   39.36 +995	0.08938
   39.37 +1019	0.08388
   39.38 +1022	0.09024
   39.39 +1046	0.10398
   39.40 +1049	0.09606
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   39.43 +1076	0.09632
   39.44 +1097	0.10336
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   39.51 +1271	0.10648
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   39.54 +1312	0.1157
   39.55 +1356	0.121
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   39.57 +1502	0.1202
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   39.92 +2222	0.16368
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  39.170 +3582	0.27796
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  39.174 +3623	0.27624
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  39.178 +3829	0.26614
  39.179 +3839	0.24278
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  39.182 +4025	0.26646
  39.183 +4083	0.27828
  39.184 +4156	0.29144
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  39.186 +4220	0.29321
  39.187 +4244	0.28512
  39.188 +4283	0.28268
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  39.191 +4389	0.27392
  39.192 +4421	0.31734
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  39.195 +4531	0.3376
  39.196 +4532	0.3211
  39.197 +4568	0.29644
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  39.199 +4582	0.3111
  39.200 +4604	0.3361
  39.201 +4629	0.321
  39.202 +4710	0.32234
  39.203 +4713	0.31781
  39.204 +4797	0.31494
  39.205 +4879	0.32866
  39.206 +4970	0.31788
  39.207 +5059	0.34627
  39.208 +5126	0.34386
  39.209 +5241	0.3861
  39.210 +5254	0.37372
  39.211 +5271	0.3535
  39.212 +5318	0.39526
  39.213 +5346	0.36535
  39.214 +5455	0.35236
  39.215 +5492	0.37942
  39.216 +5608	0.38386
  39.217 +5735	0.36456
  39.218 +5775	0.3948
  39.219 +5777	0.38222
  39.220 +5795	0.3793
  39.221 +5845	0.39406
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  39.224 +5945	0.40022
  39.225 +5974	0.390287
  39.226 +5976	0.37616
  39.227 +5983	0.3971
  39.228 +6261	0.44904
  39.229 +6606	0.44954
  39.230 +6713	0.40918
  39.231 +6778	0.40436
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  39.233 +7349	0.57651
  39.234 +7453	0.51404
  39.235 +9114	0.63858
  39.236 +9174	0.5835
  39.237 +10081	0.62952
    40.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    40.2 +++ b/VF2PPLabel/Proteins.16.txt	Tue Nov 22 08:15:16 2016 +0100
    40.3 @@ -0,0 +1,234 @@
    40.4 +535	0.11145
    40.5 +554	0.10798
    40.6 +571	0.11841
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   40.13 +734	0.14764
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   40.16 +755	0.15408
   40.17 +760	0.14146
   40.18 +788	0.154957
   40.19 +794	0.15147
   40.20 +795	0.15214
   40.21 +802	0.16778
   40.22 +816	0.15626
   40.23 +819	0.16602
   40.24 +831	0.15536
   40.25 +833	0.1655
   40.26 +838	0.1628
   40.27 +858	0.16346
   40.28 +861	0.171
   40.29 +874	0.17852
   40.30 +877	0.16644
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   40.33 +899	0.16828
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   40.36 +995	0.19202
   40.37 +1019	0.1969
   40.38 +1022	0.24424
   40.39 +1046	0.201527
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   40.43 +1076	0.2011
   40.44 +1097	0.20204
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   40.51 +1271	0.25636
   40.52 +1300	0.26922
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  40.148 +3209	0.63064
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  40.154 +3459	0.71168
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  40.158 +3502	0.71152
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  40.166 +3560	0.7119
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  40.170 +3582	0.72846
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  40.178 +3829	0.73305
  40.179 +3839	0.73132
  40.180 +3870	0.75654
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  40.182 +4025	0.77806
  40.183 +4083	0.8419
  40.184 +4156	0.83694
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  40.191 +4389	0.87538
  40.192 +4421	0.90432
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  40.194 +4521	0.88302
  40.195 +4531	0.89242
  40.196 +4532	0.8704
  40.197 +4568	0.8437
  40.198 +4573	0.87244
  40.199 +4582	0.93408
  40.200 +4604	0.9359
  40.201 +4629	0.930927
  40.202 +4710	0.96852
  40.203 +4713	0.9438
  40.204 +4797	0.91558
  40.205 +4879	0.97514
  40.206 +4970	0.98212
  40.207 +5059	1.00667
  40.208 +5126	1.0199
  40.209 +5241	1.02134
  40.210 +5254	1.01786
  40.211 +5271	1.05558
  40.212 +5318	1.02432
  40.213 +5346	1.07239
  40.214 +5455	1.10124
  40.215 +5492	1.10132
  40.216 +5608	1.12804
  40.217 +5735	1.11592
  40.218 +5775	1.18162
  40.219 +5777	1.1788
  40.220 +5795	1.18656
  40.221 +5845	1.14806
  40.222 +5859	1.08982
  40.223 +5877	1.17527
  40.224 +5945	1.19952
  40.225 +5974	1.17872
  40.226 +5976	1.17286
  40.227 +5983	1.21666
  40.228 +6261	1.27299
  40.229 +6606	1.3041
  40.230 +6713	1.35584
  40.231 +6778	1.30678
  40.232 +6883	1.36806
  40.233 +7349	1.48099
  40.234 +7453	1.44448
  40.235 +9114	1.81652
  40.236 +9174	1.82116
  40.237 +10081	1.9654
    41.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    41.2 +++ b/VF2PPLabel/Proteins.256.txt	Tue Nov 22 08:15:16 2016 +0100
    41.3 @@ -0,0 +1,234 @@
    41.4 +535	0.06895
    41.5 +554	0.0722
    41.6 +571	0.07721
    41.7 +614	0.07426
    41.8 +634	0.0742
    41.9 +636	0.11452
   41.10 +639	0.07864
   41.11 +730	0.0777
   41.12 +731	0.09782
   41.13 +734	0.0917
   41.14 +735	0.07122
   41.15 +737	0.08446
   41.16 +755	0.07262
   41.17 +760	0.07516
   41.18 +788	0.0834067
   41.19 +794	0.088265
   41.20 +795	0.07964
   41.21 +802	0.07614
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  41.166 +3560	0.1291
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  41.170 +3582	0.38224
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  41.174 +3623	0.13082
  41.175 +3703	0.16478
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  41.178 +3829	0.24891
  41.179 +3839	0.1366
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  41.183 +4083	0.15194
  41.184 +4156	0.13858
  41.185 +4194	0.13821
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  41.196 +4532	0.167633
  41.197 +4568	0.1609
  41.198 +4573	0.17246
  41.199 +4582	0.15314
  41.200 +4604	0.14972
  41.201 +4629	0.15589
  41.202 +4710	0.211
  41.203 +4713	0.17023
  41.204 +4797	0.14978
  41.205 +4879	0.16594
  41.206 +4970	0.1539
  41.207 +5059	0.17644
  41.208 +5126	0.16842
  41.209 +5241	0.15484
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  41.211 +5271	0.17262
  41.212 +5318	0.18286
  41.213 +5346	0.15306
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  41.215 +5492	0.1981
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  41.219 +5777	0.18924
  41.220 +5795	0.18758
  41.221 +5845	0.17726
  41.222 +5859	0.57416
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  41.225 +5974	0.18096
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  41.235 +9114	0.24952
  41.236 +9174	0.24266
  41.237 +10081	0.26348
    42.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    42.2 +++ b/VF2PPLabel/Proteins.32.txt	Tue Nov 22 08:15:16 2016 +0100
    42.3 @@ -0,0 +1,234 @@
    42.4 +535	0.11193
    42.5 +554	0.10556
    42.6 +571	0.11329
    42.7 +614	0.120647
    42.8 +634	0.1311
    42.9 +636	0.0938
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   42.13 +734	0.16594
   42.14 +735	0.15922
   42.15 +737	0.16158
   42.16 +755	0.16682
   42.17 +760	0.14626
   42.18 +788	0.15367
   42.19 +794	0.158275
   42.20 +795	0.16854
   42.21 +802	0.15054
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   42.25 +833	0.17666
   42.26 +838	0.13584
   42.27 +858	0.17086
   42.28 +861	0.1764
   42.29 +874	0.17336
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   42.35 +982	0.19414
   42.36 +995	0.20024
   42.37 +1019	0.19716
   42.38 +1022	0.20372
   42.39 +1046	0.209773
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   42.46 +1156	0.25694
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  42.184 +4156	0.842
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  42.200 +4604	0.9426
  42.201 +4629	0.964557
  42.202 +4710	1.03562
  42.203 +4713	1.0169
  42.204 +4797	0.92934
  42.205 +4879	0.99944
  42.206 +4970	1.05264
  42.207 +5059	1.06508
  42.208 +5126	1.0146
  42.209 +5241	1.03944
  42.210 +5254	1.03928
  42.211 +5271	1.09182
  42.212 +5318	1.09184
  42.213 +5346	1.07963
  42.214 +5455	1.09918
  42.215 +5492	1.15718
  42.216 +5608	1.17928
  42.217 +5735	1.16742
  42.218 +5775	1.22874
  42.219 +5777	1.24946
  42.220 +5795	1.1902
  42.221 +5845	1.16496
  42.222 +5859	1.20206
  42.223 +5877	1.22827
  42.224 +5945	1.23716
  42.225 +5974	1.2245
  42.226 +5976	1.19772
  42.227 +5983	1.21464
  42.228 +6261	1.32684
  42.229 +6606	1.3455
  42.230 +6713	1.44988
  42.231 +6778	1.34132
  42.232 +6883	1.42272
  42.233 +7349	1.52318
  42.234 +7453	1.5572
  42.235 +9114	1.8853
  42.236 +9174	1.90576
  42.237 +10081	2.04208
    43.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    43.2 +++ b/VF2PPLabel/Proteins.64.txt	Tue Nov 22 08:15:16 2016 +0100
    43.3 @@ -0,0 +1,234 @@
    43.4 +535	0.10953
    43.5 +554	0.12774
    43.6 +571	0.11102
    43.7 +614	0.136293
    43.8 +634	0.11158
    43.9 +636	0.08476
   43.10 +639	0.12422
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   43.13 +734	0.13628
   43.14 +735	0.12912
   43.15 +737	0.13948
   43.16 +755	0.13646
   43.17 +760	0.14376
   43.18 +788	0.144847
   43.19 +794	0.14343
   43.20 +795	0.14596
   43.21 +802	0.17388
   43.22 +816	0.10458
   43.23 +819	0.1465
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   43.25 +833	0.1618
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   43.27 +858	0.15878
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   43.29 +874	0.15302
   43.30 +877	0.14436
   43.31 +879	0.1081
   43.32 +886	0.16224
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   43.34 +957	0.16844
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   43.40 +1049	0.19474
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    44.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    44.2 +++ b/VF2PPLabel/Proteins.8.txt	Tue Nov 22 08:15:16 2016 +0100
    44.3 @@ -0,0 +1,234 @@
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    45.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    45.2 +++ b/VF2PPLabel/Proteins.txt	Tue Nov 22 08:15:16 2016 +0100
    45.3 @@ -0,0 +1,234 @@
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  45.217 +5735	0.000868944
  45.218 +5775	0.000899067
  45.219 +5777	0.000899172
  45.220 +5795	0.000895144
  45.221 +5845	0.000874161
  45.222 +5859	0.000964261
  45.223 +5877	0.00091312
  45.224 +5945	0.000910194
  45.225 +5974	0.000904886
  45.226 +5976	0.000907439
  45.227 +5983	0.000909833
  45.228 +6261	0.000970569
  45.229 +6606	0.00101129
  45.230 +6713	0.00102107
  45.231 +6778	0.000996328
  45.232 +6883	0.00103448
  45.233 +7349	0.00112629
  45.234 +7453	0.00109389
  45.235 +9114	0.00139614
  45.236 +9174	0.00136449
  45.237 +10081	0.00148714
    46.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    46.2 +++ b/VF2PPLabel/contactMapIso.txt	Tue Nov 22 08:15:16 2016 +0100
    46.3 @@ -0,0 +1,90 @@
    46.4 +99	0.344
    46.5 +102	0.385
    46.6 +104	0.415
    46.7 +105	0.38
    46.8 +107	0.366
    46.9 +114	0.353
   46.10 +117	0.394
   46.11 +120	0.452
   46.12 +122	0.478
   46.13 +123	0.451
   46.14 +124	0.385
   46.15 +125	0.517
   46.16 +130	0.508
   46.17 +133	0.509
   46.18 +136	0.533
   46.19 +137	0.552
   46.20 +138	0.532
   46.21 +140	0.584
   46.22 +141	0.561
   46.23 +144	0.552
   46.24 +146	0.273
   46.25 +147	0.505
   46.26 +149	0.448
   46.27 +150	0.529
   46.28 +151	0.538
   46.29 +156	0.615
   46.30 +157	0.638
   46.31 +158	0.651
   46.32 +159	0.597
   46.33 +162	0.647
   46.34 +164	0.581
   46.35 +169	0.666
   46.36 +181	0.656
   46.37 +185	0.793
   46.38 +186	0.787
   46.39 +187	0.724
   46.40 +190	0.803
   46.41 +191	0.796
   46.42 +192	0.82
   46.43 +193	0.826
   46.44 +197	0.825
   46.45 +198	0.833
   46.46 +199	0.865
   46.47 +214	0.812
   46.48 +220	0.914
   46.49 +221	0.903
   46.50 +222	0.951
   46.51 +224	0.926
   46.52 +225	0.945
   46.53 +226	0.958
   46.54 +228	1.007
   46.55 +237	1.019
   46.56 +252	1.067
   46.57 +264	1.151
   46.58 +265	1.067
   46.59 +271	1.153
   46.60 +274	1.279
   46.61 +275	1.384
   46.62 +276	1.213
   46.63 +277	1.227
   46.64 +280	1.235
   46.65 +286	1.254
   46.66 +302	1.442
   46.67 +327	1.425
   46.68 +330	1.49
   46.69 +334	1.581
   46.70 +336	1.513
   46.71 +359	1.689
   46.72 +360	1.712
   46.73 +385	1.627
   46.74 +387	1.68
   46.75 +388	1.684
   46.76 +393	1.681
   46.77 +395	1.715
   46.78 +414	1.797
   46.79 +428	2.109
   46.80 +457	2.107
   46.81 +484	2.438
   46.82 +501	2.318
   46.83 +556	2.314
   46.84 +558	2.252
   46.85 +564	2.707
   46.86 +585	2.601
   46.87 +599	2.643
   46.88 +600	2.56
   46.89 +611	2.957
   46.90 +617	2.616
   46.91 +694	3.851
   46.92 +741	3.578
   46.93 +773	2.433
    47.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    47.2 +++ b/VF2PPLabel/contactMapsIso.txt	Tue Nov 22 08:15:16 2016 +0100
    47.3 @@ -0,0 +1,90 @@
    47.4 +99	0.0291
    47.5 +102	0.0328
    47.6 +104	0.0368
    47.7 +105	0.0354
    47.8 +107	0.0324
    47.9 +114	0.0306
   47.10 +117	0.035
   47.11 +120	0.0411
   47.12 +122	0.042
   47.13 +123	0.039
   47.14 +124	0.034
   47.15 +125	0.0448
   47.16 +130	0.047
   47.17 +133	0.0468
   47.18 +136	0.0497
   47.19 +137	0.0474
   47.20 +138	0.0486
   47.21 +140	0.0554
   47.22 +141	0.0523
   47.23 +144	0.0502
   47.24 +146	0.0251
   47.25 +147	0.0468
   47.26 +149	0.0398
   47.27 +150	0.0492
   47.28 +151	0.0467
   47.29 +156	0.0567
   47.30 +157	0.0584
   47.31 +158	0.0573
   47.32 +159	0.0572
   47.33 +162	0.0556
   47.34 +164	0.0497
   47.35 +169	0.061
   47.36 +181	0.0565
   47.37 +185	0.0713
   47.38 +186	0.0713
   47.39 +187	0.0643
   47.40 +190	0.0721
   47.41 +191	0.0699
   47.42 +192	0.0715
   47.43 +193	0.1412
   47.44 +197	0.0747
   47.45 +198	0.0757
   47.46 +199	0.0739
   47.47 +214	0.0725
   47.48 +220	0.083
   47.49 +221	0.0828
   47.50 +222	0.0868
   47.51 +224	0.0831
   47.52 +225	0.0857
   47.53 +226	0.0844
   47.54 +228	0.0893
   47.55 +237	0.0897
   47.56 +252	0.0963
   47.57 +264	0.103
   47.58 +265	0.0965
   47.59 +271	0.1004
   47.60 +274	0.1138
   47.61 +275	0.1237
   47.62 +276	0.109
   47.63 +277	0.1116
   47.64 +280	0.1106
   47.65 +286	0.11
   47.66 +302	0.124
   47.67 +327	0.1235
   47.68 +330	0.1251
   47.69 +334	0.1409
   47.70 +336	0.1261
   47.71 +359	0.1459
   47.72 +360	0.1512
   47.73 +385	0.1452
   47.74 +387	0.1501
   47.75 +388	0.1469
   47.76 +393	0.1488
   47.77 +395	0.1523
   47.78 +414	0.1563
   47.79 +428	0.18
   47.80 +457	0.1943
   47.81 +484	0.2123
   47.82 +501	0.1909
   47.83 +556	0.2064
   47.84 +558	0.2014
   47.85 +564	0.2397
   47.86 +585	0.2323
   47.87 +599	0.2355
   47.88 +600	0.2311
   47.89 +611	0.2585
   47.90 +617	0.2293
   47.91 +694	0.3452
   47.92 +741	0.3004
   47.93 +773	0.2149
    48.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    48.2 +++ b/VF2PPLabel/moleculeIso.txt	Tue Nov 22 08:15:16 2016 +0100
    48.3 @@ -0,0 +1,91 @@
    48.4 +8	0.007
    48.5 +10	0.007
    48.6 +11	0.01
    48.7 +12	0.01
    48.8 +13	0.007
    48.9 +14	0.01
   48.10 +15	0.012
   48.11 +16	0.009
   48.12 +17	0.016
   48.13 +18	0.009
   48.14 +19	0.008
   48.15 +20	0.013
   48.16 +21	0.014
   48.17 +22	0.013
   48.18 +23	0.014
   48.19 +24	0.013
   48.20 +25	0.023
   48.21 +26	0.016
   48.22 +27	0.015
   48.23 +28	0.018
   48.24 +29	0.02
   48.25 +30	0.017
   48.26 +31	0.02
   48.27 +32	0.021
   48.28 +33	0.027
   48.29 +34	0.023
   48.30 +35	0.021
   48.31 +36	0.026
   48.32 +37	0.025
   48.33 +38	0.028
   48.34 +39	0.026
   48.35 +40	0.026
   48.36 +41	0.03
   48.37 +42	0.031
   48.38 +43	0.024
   48.39 +44	0.029
   48.40 +45	0.027
   48.41 +46	0.034
   48.42 +47	0.028
   48.43 +48	0.031
   48.44 +49	0.031
   48.45 +50	0.027
   48.46 +51	0.034
   48.47 +52	0.042
   48.48 +53	0.031
   48.49 +54	0.032
   48.50 +55	0.04
   48.51 +56	0.026
   48.52 +57	0.03
   48.53 +58	0.039
   48.54 +59	0.037
   48.55 +60	0.036
   48.56 +61	0.038
   48.57 +62	0.044
   48.58 +63	0.048
   48.59 +64	0.035
   48.60 +65	0.057
   48.61 +66	0.051
   48.62 +67	0.055
   48.63 +68	0.055
   48.64 +69	0.039
   48.65 +70	0.038
   48.66 +71	0.083
   48.67 +72	0.039
   48.68 +73	0.042
   48.69 +74	0.037
   48.70 +75	0.035
   48.71 +76	0.047
   48.72 +77	0.043
   48.73 +78	0.046
   48.74 +79	0.041
   48.75 +80	0.048
   48.76 +81	0.049
   48.77 +82	0.05
   48.78 +83	0.048
   48.79 +84	0.048
   48.80 +85	0.048
   48.81 +86	0.062
   48.82 +87	0.069
   48.83 +88	0.055
   48.84 +89	0.056
   48.85 +90	0.087
   48.86 +91	0.049
   48.87 +92	0.26
   48.88 +93	0.046
   48.89 +94	0.058
   48.90 +95	0.059
   48.91 +96	0.054
   48.92 +97	0.056
   48.93 +98	0.057
   48.94 +99	0.085
    49.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    49.2 +++ b/VF2PPLabel/moleculesIso.txt	Tue Nov 22 08:15:16 2016 +0100
    49.3 @@ -0,0 +1,89 @@
    49.4 +8	0.0019
    49.5 +10	0.00257
    49.6 +11	0.00364
    49.7 +12	0.00439
    49.8 +13	0.00295
    49.9 +14	0.00355
   49.10 +15	0.00532
   49.11 +16	0.00328
   49.12 +17	0.00545
   49.13 +18	0.00405
   49.14 +19	0.00366
   49.15 +20	0.00578
   49.16 +21	0.00626
   49.17 +22	0.00552
   49.18 +23	0.00709
   49.19 +24	0.00582
   49.20 +25	0.01599
   49.21 +26	0.00792
   49.22 +27	0.00664
   49.23 +28	0.01131
   49.24 +29	0.01014
   49.25 +30	0.00954
   49.26 +31	0.00928
   49.27 +32	0.01455
   49.28 +33	0.01275
   49.29 +34	0.01112
   49.30 +35	0.01015
   49.31 +36	0.01282
   49.32 +37	0.01194
   49.33 +38	0.01299
   49.34 +39	0.01654
   49.35 +40	0.01254
   49.36 +41	0.01721
   49.37 +42	0.01529
   49.38 +43	0.01145
   49.39 +44	0.0148
   49.40 +45	0.0143
   49.41 +46	0.01607
   49.42 +47	0.01371
   49.43 +48	0.01659
   49.44 +49	0.01326
   49.45 +50	0.01207
   49.46 +51	0.01749
   49.47 +52	0.01659
   49.48 +53	0.01402
   49.49 +54	0.01436
   49.50 +55	0.01682
   49.51 +56	0.01272
   49.52 +57	0.01363
   49.53 +58	0.01681
   49.54 +59	0.01931
   49.55 +60	0.0167
   49.56 +61	0.02353
   49.57 +62	0.02156
   49.58 +63	0.02237
   49.59 +64	0.01871
   49.60 +65	0.02711
   49.61 +66	0.02543
   49.62 +67	0.02564
   49.63 +68	0.02756
   49.64 +69	0.01824
   49.65 +70	0.01886
   49.66 +71	0.03311
   49.67 +72	0.01855
   49.68 +73	0.02787
   49.69 +74	0.01942
   49.70 +75	0.01862
   49.71 +76	0.02026
   49.72 +77	0.02185
   49.73 +78	0.02233
   49.74 +79	0.02119
   49.75 +80	0.02483
   49.76 +81	0.02532
   49.77 +82	0.02191
   49.78 +83	0.02626
   49.79 +84	0.02757
   49.80 +85	0.0208
   49.81 +86	0.02836
   49.82 +87	0.0255
   49.83 +88	0.02559
   49.84 +89	0.02899
   49.85 +91	0.02606
   49.86 +93	0.02955
   49.87 +94	0.02854
   49.88 +95	0.0314
   49.89 +96	0.02446
   49.90 +97	0.02558
   49.91 +98	0.02757
   49.92 +99	0.03396
    50.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    50.2 +++ b/VF2PPLabel/proteinIso.txt	Tue Nov 22 08:15:16 2016 +0100
    50.3 @@ -0,0 +1,234 @@
    50.4 +535	0.236
    50.5 +554	0.24
    50.6 +571	0.289
    50.7 +614	0.246
    50.8 +634	0.27
    50.9 +636	0.321
   50.10 +639	0.274
   50.11 +730	0.334
   50.12 +731	0.316
   50.13 +734	0.428
   50.14 +735	0.309
   50.15 +737	0.495
   50.16 +755	0.305
   50.17 +760	0.359
   50.18 +788	0.421
   50.19 +794	0.467
   50.20 +795	0.375
   50.21 +802	0.333
   50.22 +816	0.34
   50.23 +819	0.387
   50.24 +831	0.355
   50.25 +833	0.366
   50.26 +838	0.354
   50.27 +858	0.357
   50.28 +861	0.503
   50.29 +874	0.353
   50.30 +877	0.362
   50.31 +879	0.497
   50.32 +886	0.42
   50.33 +899	0.44
   50.34 +957	0.399
   50.35 +982	0.475
   50.36 +995	0.415
   50.37 +1019	3.067
   50.38 +1022	0.964
   50.39 +1046	0.477
   50.40 +1049	0.442
   50.41 +1060	0.447
   50.42 +1073	0.677
   50.43 +1076	0.459
   50.44 +1097	0.461
   50.45 +1140	0.509
   50.46 +1156	0.604
   50.47 +1183	0.492
   50.48 +1192	0.534
   50.49 +1202	0.557
   50.50 +1227	0.63
   50.51 +1271	0.652
   50.52 +1300	0.539
   50.53 +1304	0.541
   50.54 +1312	0.607
   50.55 +1356	0.71
   50.56 +1494	0.658
   50.57 +1502	1.021
   50.58 +1559	0.64
   50.59 +1568	0.665
   50.60 +1576	0.702
   50.61 +1605	1.342
   50.62 +1608	1.443
   50.63 +1625	0.721
   50.64 +1632	0.691
   50.65 +1635	0.899
   50.66 +1648	0.812
   50.67 +1674	0.703
   50.68 +1684	0.711
   50.69 +1732	0.729
   50.70 +1744	1.074
   50.71 +1750	1.325
   50.72 +1754	0.895
   50.73 +1764	0.744
   50.74 +1775	0.734
   50.75 +1826	2.625
   50.76 +1844	0.91
   50.77 +1886	1.032
   50.78 +1930	0.906
   50.79 +1938	0.977
   50.80 +1948	0.807
   50.81 +1995	0.837
   50.82 +2000	1.037
   50.83 +2020	0.873
   50.84 +2044	0.883
   50.85 +2086	1.118
   50.86 +2115	0.906
   50.87 +2123	1.044
   50.88 +2126	1.034
   50.89 +2138	0.907
   50.90 +2168	1.424
   50.91 +2190	8.243
   50.92 +2222	8.425
   50.93 +2250	0.972
   50.94 +2298	0.979
   50.95 +2314	0.958
   50.96 +2316	1.092
   50.97 +2325	1.094
   50.98 +2327	0.977
   50.99 +2329	2.405
  50.100 +2344	1.097
  50.101 +2348	1.239
  50.102 +2355	0.999
  50.103 +2379	1.542
  50.104 +2383	0.999
  50.105 +2413	1.16
  50.106 +2423	1.014
  50.107 +2464	1.079
  50.108 +2466	1.042
  50.109 +2512	1.184
  50.110 +2546	1.143
  50.111 +2553	1.236
  50.112 +2593	1.172
  50.113 +2604	1.223
  50.114 +2605	1.295
  50.115 +2607	1.192
  50.116 +2610	1.189
  50.117 +2611	2
  50.118 +2612	1.241
  50.119 +2613	1.326
  50.120 +2616	1.12
  50.121 +2620	1.532
  50.122 +2622	1.219
  50.123 +2625	1.419
  50.124 +2648	1.094
  50.125 +2651	1.104
  50.126 +2716	1.268
  50.127 +2733	1.612
  50.128 +2775	5.068
  50.129 +2812	1.259
  50.130 +2838	1.492
  50.131 +2857	1.398
  50.132 +2872	1.215
  50.133 +2887	1.626
  50.134 +2916	1.352
  50.135 +2920	1.254
  50.136 +2928	1.438
  50.137 +2949	1.315
  50.138 +2966	1.268
  50.139 +2977	1.848
  50.140 +2991	1.398
  50.141 +3104	1.326
  50.142 +3130	1.452
  50.143 +3131	1.416
  50.144 +3134	1.401
  50.145 +3135	1.348
  50.146 +3172	1.497
  50.147 +3182	1.428
  50.148 +3209	1.505
  50.149 +3243	1.409
  50.150 +3255	1.49
  50.151 +3310	1.461
  50.152 +3366	1.635
  50.153 +3429	2.107
  50.154 +3459	1.46
  50.155 +3469	1.481
  50.156 +3483	1.598
  50.157 +3497	1.803
  50.158 +3502	1.552
  50.159 +3505	1.794
  50.160 +3515	1.644
  50.161 +3517	1.531
  50.162 +3522	1.494
  50.163 +3523	1.776
  50.164 +3526	1.829
  50.165 +3529	1.495
  50.166 +3560	1.528
  50.167 +3563	1.851
  50.168 +3566	1.554
  50.169 +3574	1.678
  50.170 +3582	1.609
  50.171 +3584	1.617
  50.172 +3618	1.668
  50.173 +3619	1.717
  50.174 +3623	1.656
  50.175 +3703	1.579
  50.176 +3711	1.668
  50.177 +3819	2.668
  50.178 +3829	1.704
  50.179 +3839	1.865
  50.180 +3870	1.939
  50.181 +3906	1.673
  50.182 +4025	2.308
  50.183 +4083	2.043
  50.184 +4156	1.911
  50.185 +4194	2.312
  50.186 +4220	2.417
  50.187 +4244	2.195
  50.188 +4283	2.477
  50.189 +4353	1.875
  50.190 +4382	1.92
  50.191 +4389	2.067
  50.192 +4421	2.074
  50.193 +4446	2.504
  50.194 +4521	2.222
  50.195 +4531	2.165
  50.196 +4532	2.168
  50.197 +4568	2.7
  50.198 +4573	2.494
  50.199 +4582	2.02
  50.200 +4604	3.078
  50.201 +4629	2.512
  50.202 +4710	2.4
  50.203 +4713	2.178
  50.204 +4797	2.278
  50.205 +4879	2.542
  50.206 +4970	2.115
  50.207 +5059	2.188
  50.208 +5126	2.209
  50.209 +5241	2.311
  50.210 +5254	2.738
  50.211 +5271	2.336
  50.212 +5318	2.791
  50.213 +5346	2.37
  50.214 +5455	2.647
  50.215 +5492	2.404
  50.216 +5608	2.594
  50.217 +5735	2.837
  50.218 +5775	2.667
  50.219 +5777	2.541
  50.220 +5795	3.983
  50.221 +5845	2.654
  50.222 +5859	3.366
  50.223 +5877	3.159
  50.224 +5945	2.893
  50.225 +5974	3.353
  50.226 +5976	2.664
  50.227 +5983	3.436
  50.228 +6261	3.986
  50.229 +6606	2.913
  50.230 +6713	2.994
  50.231 +6778	3.711
  50.232 +6883	2.973
  50.233 +7349	3.269
  50.234 +7453	3.998
  50.235 +9114	4.116
  50.236 +9174	5.284
  50.237 +10081	4.765
    51.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    51.2 +++ b/VF2PPLabel/proteinsIso.txt	Tue Nov 22 08:15:16 2016 +0100
    51.3 @@ -0,0 +1,234 @@
    51.4 +535	0.0196
    51.5 +554	0.02
    51.6 +571	0.0206
    51.7 +614	0.0216
    51.8 +634	0.0236
    51.9 +636	0.0278
   51.10 +639	0.0253
   51.11 +730	0.0285
   51.12 +731	0.0273
   51.13 +734	0.0284
   51.14 +735	0.0263
   51.15 +737	0.0403
   51.16 +755	0.0267
   51.17 +760	0.027
   51.18 +788	0.0392
   51.19 +794	0.0353
   51.20 +795	0.0333
   51.21 +802	0.0291
   51.22 +816	0.0293
   51.23 +819	0.0323
   51.24 +831	0.0307
   51.25 +833	0.0315
   51.26 +838	0.032
   51.27 +858	0.0307
   51.28 +861	0.0414
   51.29 +874	0.0311
   51.30 +877	0.0314
   51.31 +879	0.0482
   51.32 +886	0.0325
   51.33 +899	0.0417
   51.34 +957	0.0342
   51.35 +982	0.0419
   51.36 +995	0.036
   51.37 +1019	0.3185
   51.38 +1022	0.0953
   51.39 +1046	0.0413
   51.40 +1049	0.0383
   51.41 +1060	0.0392
   51.42 +1073	0.0602
   51.43 +1076	0.0391
   51.44 +1097	0.0396
   51.45 +1140	0.0457
   51.46 +1156	0.0544
   51.47 +1183	0.0433
   51.48 +1192	0.0465
   51.49 +1202	0.0443
   51.50 +1227	0.0565
   51.51 +1271	0.0568
   51.52 +1300	0.047
   51.53 +1304	0.0471
   51.54 +1312	0.0493
   51.55 +1356	0.0673
   51.56 +1494	0.0571
   51.57 +1502	0.0996
   51.58 +1559	0.0561
   51.59 +1568	0.0587
   51.60 +1576	0.0567
   51.61 +1605	0.1319
   51.62 +1608	0.128
   51.63 +1625	0.0585
   51.64 +1632	0.0599
   51.65 +1635	0.0744
   51.66 +1648	0.0614
   51.67 +1674	0.0609
   51.68 +1684	0.0617
   51.69 +1732	0.0625
   51.70 +1744	0.0987
   51.71 +1750	0.1193
   51.72 +1754	0.0673
   51.73 +1764	0.064
   51.74 +1775	0.0638
   51.75 +1826	0.2566
   51.76 +1844	0.0712
   51.77 +1886	0.0681
   51.78 +1930	0.0861
   51.79 +1938	0.0883
   51.80 +1948	0.0702
   51.81 +1995	0.0724
   51.82 +2000	0.0808
   51.83 +2020	0.0772
   51.84 +2044	0.0781
   51.85 +2086	0.0962
   51.86 +2115	0.0807
   51.87 +2123	0.095
   51.88 +2126	0.0897
   51.89 +2138	0.0773
   51.90 +2168	0.1222
   51.91 +2190	1.1356
   51.92 +2222	1.1137
   51.93 +2250	0.0864
   51.94 +2298	0.0883
   51.95 +2314	0.0822
   51.96 +2316	0.0969
   51.97 +2325	0.092
   51.98 +2327	0.0872
   51.99 +2329	0.2248
  51.100 +2344	0.0992
  51.101 +2348	0.1149
  51.102 +2355	0.0882
  51.103 +2379	0.1295
  51.104 +2383	0.0902
  51.105 +2413	0.1051
  51.106 +2423	0.0887
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  51.113 +2604	0.1105
  51.114 +2605	0.1104
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  51.116 +2610	0.112
  51.117 +2611	0.2361
  51.118 +2612	0.0993
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  51.120 +2616	0.097
  51.121 +2620	0.1461
  51.122 +2622	0.1106
  51.123 +2625	0.1103
  51.124 +2648	0.0962
  51.125 +2651	0.0972
  51.126 +2716	0.1141
  51.127 +2733	0.1456
  51.128 +2775	0.5155
  51.129 +2812	0.1058
  51.130 +2838	0.1357
  51.131 +2857	0.1268
  51.132 +2872	0.1107
  51.133 +2887	0.1461
  51.134 +2916	0.1217
  51.135 +2920	0.1091
  51.136 +2928	0.1265
  51.137 +2949	0.1168
  51.138 +2966	0.1171
  51.139 +2977	0.1667
  51.140 +2991	0.1162
  51.141 +3104	0.1168
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  51.143 +3131	0.1263
  51.144 +3134	0.122
  51.145 +3135	0.1234
  51.146 +3172	0.1239
  51.147 +3182	0.1196
  51.148 +3209	0.1311
  51.149 +3243	0.1222
  51.150 +3255	0.1266
  51.151 +3310	0.1293
  51.152 +3366	0.1315
  51.153 +3429	0.2286
  51.154 +3459	0.1276
  51.155 +3469	0.1283
  51.156 +3483	0.2306
  51.157 +3497	0.1612
  51.158 +3502	0.1395
  51.159 +3505	0.1615
  51.160 +3515	0.1494
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  51.162 +3522	0.1333
  51.163 +3523	0.1634
  51.164 +3526	0.1611
  51.165 +3529	0.1337
  51.166 +3560	0.1339
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  51.168 +3566	0.1368
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  51.170 +3582	0.1349
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  51.172 +3618	0.1363
  51.173 +3619	0.1521
  51.174 +3623	0.1349
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  51.176 +3711	0.1441
  51.177 +3819	0.2479
  51.178 +3829	0.1483
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  51.180 +3870	0.1721
  51.181 +3906	0.1537
  51.182 +4025	0.2162
  51.183 +4083	0.1807
  51.184 +4156	0.1582
  51.185 +4194	0.2017
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  51.189 +4353	0.1692
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  51.201 +4629	0.2356
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  51.203 +4713	0.186
  51.204 +4797	0.1976
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  51.207 +5059	0.1984
  51.208 +5126	0.2013
  51.209 +5241	0.2036
  51.210 +5254	0.242
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  51.227 +5983	0.3043
  51.228 +6261	0.3742
  51.229 +6606	0.2604
  51.230 +6713	0.2639
  51.231 +6778	0.2694
  51.232 +6883	0.2669
  51.233 +7349	0.2932
  51.234 +7453	0.369
  51.235 +9114	0.3689
  51.236 +9174	0.5011
  51.237 +10081	0.398
    52.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    52.2 +++ b/bibliography.bib	Tue Nov 22 08:15:16 2016 +0100
    52.3 @@ -0,0 +1,174 @@
    52.4 +%Since BibTeX does not appear to have a built in entry
    52.5 +%for citing websites (what kind of design is that?),
    52.6 +%I decided to stick websites in with articles, and to stick
    52.7 +%the URL in the journal field. This is not technically correct.
    52.8 +%I did something largely similar with Walter Lewin's video lectures,
    52.9 +%(which are wonderful), posted online through MIT OCW. Since a
   52.10 +%'proper' way of citing it wasn't built in, I made one up. If
   52.11 +%you're doing a bibliography where correct formatting is very
   52.12 +%important, you'd do best not to follow my example. Otherwise,
   52.13 +%I think it's good enough.
   52.14 +
   52.15 +@Article{CordellaVentoSymbolRecognition,
   52.16 +  author =       "L.P. Cordella, M. Vento",
   52.17 +  title =        "Symbol recognition in documents: a collection of techniques?",
   52.18 +  journal =      "International Journal on Document Analysis and Recognition Volume 3, Issue 2, pp 73-88",
   52.19 +  year =         2000,
   52.20 +  month =        "December"
   52.21 +}
   52.22 +
   52.23 +@Article{ProteinDataBank,
   52.24 +  author =       "Protein Data Bank",
   52.25 +  title =        "http://www.rcsb.org/pdb",
   52.26 +  journal =      "",
   52.27 +  year =         2015,
   52.28 +  month =        "June"
   52.29 +}
   52.30 +
   52.31 +@Article{LEMON,
   52.32 +  author =       "LEMON: Library for Efficient Modeling and Optimization in Networks",
   52.33 +  title =        "https://lemon.cs.elte.hu",
   52.34 +  journal =      "",
   52.35 +  year =         2015,
   52.36 +  month =        "March"
   52.37 +}
   52.38 +
   52.39 +@Article{QUANTUMBIO,
   52.40 +  author =       "QuantumBio Inc.",
   52.41 +  title =        "http://www.quantumbioinc.com/"
   52.42 +}
   52.43 +
   52.44 +@Article{Content,
   52.45 +  author =       "Vento, Mario and Jiang, Xiaoyi and Foggia, Pasquale",
   52.46 +  title =        "International  contest  on pattern search in biological databases, http://biograph2014.unisa.it ",
   52.47 +  journal =      "",
   52.48 +  year =         2015,
   52.49 +  month =        "June"
   52.50 +}
   52.51 +
   52.52 +@Article{VF,
   52.53 +  author =       "L. P. Cordella, P. Foggia, C. Sansone and M. Vento",
   52.54 +  title =        "Performance Evaluation of the VF Graph Matching Algorithm",
   52.55 +  journal =      "Proc. of the 10th ICIAP, IEEE Computer Society Press, pp. 1172-1177",
   52.56 +  year =         1999,
   52.57 +  month =        ""
   52.58 +}
   52.59 +
   52.60 +@Article{UllmannBit,
   52.61 +  author =       "Julian R. Ullmann",
   52.62 +  title =        "Bit-vector algorithms for binary constraint satisfaction and subgraph isomorphism",
   52.63 +  journal =      "Journal of Experimental Algorithmics (JEA),Volume 15, Article No. 1.6, ACM New York, NY, USA ",
   52.64 +  year =         2010,
   52.65 +  month =        ""
   52.66 +}
   52.67 +
   52.68 +@Article{Ullmann,
   52.69 +  author =       "J. R. Ullmann",
   52.70 +  title =        "An Algorithm for Subgraph Isomorphism",
   52.71 +  journal =      "Journal of the ACM (JACM), Volume 23 Issue 1, Pages 31-42 ",
   52.72 +  year =         1976,
   52.73 +  month =        "January"
   52.74 +}
   52.75 +
   52.76 +@Article{SubgraphNPC,
   52.77 +  author =       "Cook, S. A.",
   52.78 +  title =        "The complexity of theorem-proving procedures",
   52.79 +  journal =      "Proc. 3rd ACM Symposium on Theory of Computing, pp. 151-158",
   52.80 +  year =         1971,
   52.81 +  month =        ""
   52.82 +}
   52.83 +
   52.84 +@Article{VF2,
   52.85 +  author =       "Cordella, L.P. and Foggia, P. and Sansone, C. and Vento, M.",
   52.86 +  title =        "A (sub)graph isomorphism algorithm for matching large graphs ",
   52.87 +  journal =      "Journal of the ACM (JACM) JACM Homepage archive Volume 23 Issue 1, Pages 31-42 ",
   52.88 +  year =         2004,
   52.89 +  month =        ""
   52.90 +}
   52.91 +
   52.92 +@Article{VF2Plus,
   52.93 +  author =       "Carletti Vincenzo and Pasquale Foggia and Mario Vento",
   52.94 +  title =        "VF2 Plus: An Improved Version of VF2 For Biological Graphs",
   52.95 +  journal =      "Conference: Graph-Based Representations in Pattern Recognition, At Beijing ",
   52.96 +  year =         2015,
   52.97 +  month =        "May"
   52.98 +}
   52.99 +
  52.100 +@Article{RI,
  52.101 +  author =       "Vincenzo Bonnici and Rosalba Giugno and Alfredo Pulvirenti and Dennis Shasha and Alfredo Ferro",
  52.102 +  title =        "A subgraph isomorphism algorithm and its application to biochemical data",
  52.103 +  journal =      "BMC Bioinformatics. 2013; 14(Suppl 7): S13. ",
  52.104 +  year =         2013,
  52.105 +  month =        "April"
  52.106 +}
  52.107 +
  52.108 +@Article{Lad,
  52.109 +  author =       "Brendan D. McKay",
  52.110 +  title =        "AllDifferent-based filtering for subgraph isomorphism",
  52.111 +  journal =      "Artificial Intelligence 174,850-864",
  52.112 +  year =         2010,
  52.113 +  month =        ""
  52.114 +}
  52.115 +@Article{Nauty,
  52.116 +  author =       "Christine Solnon",
  52.117 +  title =        "Practical Graph Isomorphism",
  52.118 +  journal =      "Congressus Numerantium, vol.30, pp. 45-87",
  52.119 +  year =         1981,
  52.120 +  month =        ""
  52.121 +}
  52.122 +
  52.123 +@Article{JianzhuangYongFaceIdentification,
  52.124 +  author = 	 "Jianzhuang Liu and Yong Tsui Lee",
  52.125 +  title = 	 "A Graph-Based Method for Face Identification from a Single 2D Line Drawing",
  52.126 +  journal = 	 "IEEE Transactions on Pattern Analysis and Machine Intelligence - Graph Algorithms and Computer Vision archive Volume 23 Issue 10",
  52.127 +  year = 	 2001,
  52.128 +  month = 	 "October"
  52.129 +}
  52.130 +
  52.131 +@Article{HorstBunkeApplications,
  52.132 +  author = 	 "Horst Bunke",
  52.133 +  title = 	 "Graph Matching: Theoretical Foundations, Algorithms, and Applications",
  52.134 +  journal = 	 "In International Conference on Vision Interface, pp. 82-84",
  52.135 +  year = 	 2000,
  52.136 +  month = 	 "May"
  52.137 +}
  52.138 +
  52.139 +@Article{AlexandruApplications,
  52.140 +  author =       "Alexandru T. Balaban",
  52.141 +  title =        "Applications of graph theory in chemistry",
  52.142 +  journal =      "J. Chem. Inf. Comput. Sci., 1985,25(3),pp 334-343",
  52.143 +  year =         1985,
  52.144 +  month =        "March"
  52.145 +}
  52.146 +
  52.147 +@Article{PlanarGraphIso,
  52.148 +  author =       "J. E. Hopcroft and J. K. Wong",
  52.149 +  title =        "Linear time algorithm for isomorphism of planar graphs",
  52.150 +  journal =      "Proceeding STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing, Pages 172-184 ",
  52.151 +  year =         1974,
  52.152 +  month =        "April"
  52.153 +}
  52.154 +
  52.155 +@Article{BondedDegGraphIso,
  52.156 +  author =       "Eugene M. Luks",
  52.157 +  title =        "Isomorphism of Graphs of Bounded Valence Can Be Tested in Polynomial Time",
  52.158 +  journal =      "Journal of Computer and System Sciences, Volume 25, Issue 1, Pages 42-65",
  52.159 +  year =         1982,
  52.160 +  month =        "August"
  52.161 +}
  52.162 +
  52.163 +@Article{IntervalGraphIso,
  52.164 +  author =       "George S. Lue and Kellogg S. Booth",
  52.165 +  title =        "A Linear Time Algorithm for Deciding Interval Graph Isomorphism",
  52.166 +  journal =      "Journal of the ACM (JACM), Volume 26, Issue 2, Pages 183-195 ",
  52.167 +  year =         1979,
  52.168 +  month =        "April"
  52.169 +}
  52.170 +
  52.171 +@Article{PermGraphIso,
  52.172 +  author =       "Charles J. Colbourn",
  52.173 +  title =        "On testing isomorphism of permutation graphs",
  52.174 +  journal =      "Networks, Volume 11, Issue 1, Pages 13-21 ",
  52.175 +  year =         1981,
  52.176 +  month =        "March"
  52.177 +}
    53.1 --- a/damecco.tex	Fri Nov 18 16:45:03 2016 +0100
    53.2 +++ b/damecco.tex	Tue Nov 22 08:15:16 2016 +0100
    53.3 @@ -47,6 +47,34 @@
    53.4  %% for the whole article with \linenumbers.
    53.5  %% \usepackage{lineno}
    53.6  
    53.7 +\usepackage{amsmath}
    53.8 +%% \usepackage[pdftex]{graphicx}
    53.9 +
   53.10 +\usepackage{pgfplots}
   53.11 +\pgfplotsset{width=9cm}
   53.12 +\pgfplotsset{compat=1.8}
   53.13 +
   53.14 +\usepackage{caption}
   53.15 +\usepackage{subcaption} 
   53.16 +
   53.17 +\usepackage{algorithm}
   53.18 +\usepackage{algpseudocode}
   53.19 +\usepackage{tikz}
   53.20 +
   53.21 +\usepackage{amsthm,amssymb}
   53.22 +\renewcommand{\qedsymbol}{\rule{0.7em}{0.7em}}
   53.23 +
   53.24 +\newtheorem{theorem}{Theorem}[subsection]
   53.25 +\newtheorem{corollary}{Corollary}[theorem]
   53.26 +\newtheorem{claim}[theorem]{Claim}
   53.27 +
   53.28 +\newtheorem{definition}{Definition}[subsection]
   53.29 +\newtheorem{notation}{Notation}[subsection]
   53.30 +\newtheorem{example}{Example}[subsection]
   53.31 +\usetikzlibrary{decorations.markings}
   53.32 +\let\oldproofname=\proofname
   53.33 +%% \renewcommand{\proofname}{\rm\bf{Proof:}}
   53.34 +
   53.35  \journal{Discrete Applied Mathematics}
   53.36  
   53.37  \begin{document}
   53.38 @@ -147,8 +175,1201 @@
   53.39  %% \linenumbers
   53.40  
   53.41  %% main text
   53.42 -\section{}
   53.43 -\label{}
   53.44 +\section{Introduction}
   53.45 +\label{sec:intro}
   53.46 +
   53.47 +In the last decades, combinatorial structures, and especially graphs have been considered with ever increasing interest, and applied to the solution of several new and revised questions.
   53.48 +The expressiveness, the simplicity and the studiedness of graphs make them practical for modelling and appear constantly in several seemingly independent fields.
   53.49 +Bioinformatics and chemistry are amongst the most relevant and most important fields.
   53.50 +
   53.51 +Complex biological systems arise from the interaction and cooperation of plenty of molecular components. Getting acquainted with such systems at the molecular level has primary importance, since protein-protein interaction, DNA-protein interaction, metabolic interaction, transcription factor binding, neuronal networks, and hormone signaling networks can be understood only this way.
   53.52 +
   53.53 +For instance, a molecular structure can be considered as a graph, whose nodes correspond to atoms and whose edges to chemical bonds. The secondary structure of a protein can also be represented as a graph, where nodes are associated with aminoacids and the edges with hydrogen bonds. The nodes are often whole molecular components and the edges represent some relationships among them.
   53.54 +The similarity and dissimilarity of objects corresponding to nodes are incorporated to the model by \emph{node labels}.
   53.55 +Many other chemical and biological structures can easily be modeled in a similar way. Understanding such networks basically requires finding specific subgraphs, which can not avoid the application of graph matching algorithms.
   53.56 +
   53.57 +Finally, let some of the other real-world fields related to some variants of graph matching be briefly mentioned: pattern recognition and machine vision \cite{HorstBunkeApplications}, symbol recognition \cite{CordellaVentoSymbolRecognition}, face identification \cite{JianzhuangYongFaceIdentification}.
   53.58 +\\
   53.59 +
   53.60 +Subgraph and induced subgraph matching problems are known to be NP-Complete\cite{SubgraphNPC}, while the graph isomorphism problem is one of the few problems in NP neither known to be in P nor NP-Complete. Although polynomial time isomorphism algorithms are known for various graph classes, like trees and planar graphs\cite{PlanarGraphIso}, bounded valence graphs\cite{BondedDegGraphIso}, interval graphs\cite{IntervalGraphIso} or permutation graphs\cite{PermGraphIso}.
   53.61 +
   53.62 +In the following, some algorithms based on other approaches are summarized, which do not need any restrictions on the graphs. However, an overall polynomial behaviour is not expectable from such an alternative, it may often have good performance, even on a graph class for which polynomial algorithm is known. Note that this summary containing only exact matching algorithms is far not complete, neither does it cover all the recent algorithms.
   53.63 +
   53.64 +The first practically usable approach was due to \textbf{Ullmann}\cite{Ullmann} which is a commonly used depth-first search based algorithm with a complex heuristic for reducing the number of visited states. A major problem is its $\Theta(n^3)$ space complexity, which makes it impractical in the case of big sparse graphs.
   53.65 +
   53.66 +In a recent paper, \textbf{Ullmann}\cite{UllmannBit} presents an improved version of this algorithm based on a bit-vector solution for the binary Constraint Satisfaction Problem.
   53.67 +
   53.68 +The \textbf{Nauty} algorithm\cite{Nauty} transforms the two graphs to a canonical form before starting to check for the isomorphism. It has been considered as one of the fastest graph isomorphism algorithms, although graph categories were shown in which it takes exponentially many steps. This algorithm handles only the graph isomorphism problem.
   53.69 +
   53.70 +The \textbf{LAD} algorithm\cite{Lad} uses a depth-first search strategy and formulates the matching as a Constraint Satisfaction Problem to prune the search tree. The constraints are that the mapping has to be injective and edge-preserving, hence it is possible to handle new matching types as well.
   53.71 +
   53.72 +The \textbf{RI} algorithm\cite{RI} and its variations are based on a state space representation. After reordering the nodes of the graphs, it uses some fast executable heuristic checks without using any complex pruning rules. It seems to run really efficiently on graphs coming from biology, and won the International Contest on Pattern Search in Biological Databases\cite{Content}. 
   53.73 +
   53.74 +The currently most commonly used algorithm is the \textbf{VF2}\cite{VF2}, the improved version of VF\cite{VF}, which was designed for solving pattern matching and computer vision problems, and has been one of the best overall algorithms for more than a decade. Although, it can't be up to new specialized algorithms, it is still widely used due to its simplicity and space efficiency. VF2 uses a state space representation and checks some conditions in each state to prune the search tree.
   53.75 +
   53.76 +Our first graph matching algorithm was the first version of VF2 which recognizes the significance of the node ordering, more opportunities to increase the cutting efficiency and reduce its computational complexity. This project was initiated and sponsored by QuantumBio Inc.\cite{QUANTUMBIO} and the implementation --- along with a source code --- has been published as a part of LEMON\cite{LEMON} open source graph library.
   53.77 +
   53.78 +This thesis introduces \textbf{VF2++}, a new further improved algorithm for the graph and (induced)subgraph isomorphism problem, which uses efficient cutting rules and determines a node order in which VF2 runs significantly faster on practical inputs.
   53.79 +
   53.80 +Meanwhile, another variant called \textbf{VF2 Plus}\cite{VF2Plus} has been published. It is considered to be as efficient as the RI algorithm and has a strictly better behavior on large graphs.  The main idea of VF2 Plus is to precompute a heuristic node order of the small graph, in which the VF2 works more efficiently.\newline
   53.81 +\newline
   53.82 +
   53.83 +\section{Problem Statement}
   53.84 +This section provides a detailed description of the problems to be solved.
   53.85 +\subsection{Definitions}
   53.86 +
   53.87 +Throughout the paper $G_{small}=(V_{small}, E_{small})$ and $G_{large}=(V_{large}, E_{large})$ denote two undirected graphs.
   53.88 +\begin{definition}\label{sec:ismorphic}
   53.89 +$G_{small}$ and $G_{large}$ are \textbf{isomorphic} if $\exists M: V_{small} \longrightarrow V_{large}$ bijection, for which the following is true:
   53.90 +\begin{center}
   53.91 +$\forall u,v\in{V_{small}} : (u,v)\in{E_{small}} \Leftrightarrow (M(u),M(v))\in{E_{large}}$
   53.92 +\end{center}
   53.93 +\end{definition}
   53.94 +For the sake of simplicity in this paper subgraphs and induced subgraphs are defined in a more general way than usual:
   53.95 +\begin{definition}
   53.96 +$G_{small}$ is a \textbf{subgraph} of $G_{large}$ if $\exists I: V_{small}\longrightarrow V_{large}$ injection, for which the following is true:
   53.97 +\begin{center}
   53.98 +$\forall u,v \in{V_{small}} : (u,v)\in{E_{small}} \Rightarrow (I(u),I(v))\in E_{large}$
   53.99 +\end{center}
  53.100 +\end{definition}
  53.101 +
  53.102 +\begin{definition} 
  53.103 +$G_{small}$ is an \textbf{induced subgraph} of $G_{large}$ if $\exists I: V_{small}\longrightarrow V_{large}$ injection, for which the following is true:
  53.104 +\begin{center}
  53.105 +$\forall u,v \in{V_{small}} : (u,v)\in{E_{small}} \Leftrightarrow (I(u),I(v))\in E_{large}$
  53.106 +\end{center}
  53.107 +\end{definition}
  53.108 +
  53.109 +\begin{definition}
  53.110 +$lab: (V_{small}\cup V_{large}) \longrightarrow K$ is a \textbf{node label function}, where K is an arbitrary set. The elements in K are the \textbf{node labels}. Two nodes, u and v are said to be \textbf{equivalent}, if $lab(u)=lab(v)$.
  53.111 +\end{definition}
  53.112 +
  53.113 +When node labels are also given, the matched nodes must have the same labels.
  53.114 +For example, the node labeled isomorphism is phrased by
  53.115 +\begin{definition}
  53.116 +$G_{small}$ and $G_{large}$ are \textbf{isomorphic by the node label function lab} if $\exists M: V_{small} \longrightarrow V_{large}$ bijection, for which the following is true:
  53.117 +\begin{center}
  53.118 +$(\forall u,v\in{V_{small}} : (u,v)\in{E_{small}} \Leftrightarrow (M(u),M(v))\in{E_{large}})$
  53.119 + and $(\forall u\in{V_{small}} : lab(u)=lab(M(u)))$
  53.120 +\end{center}
  53.121 +\end{definition}
  53.122 +
  53.123 +The other two definitions can be extended in the same way.
  53.124 +
  53.125 +Note that edge label function can be defined similarly to node label function, and all the definitions can be extended with additional conditions, but it is out of the scope of this work.
  53.126 +
  53.127 +The equivalence of two nodes is usually defined by another relation, $\\R\subseteq (V_{small}\cup V_{large})^2$. This overlaps with the definition given above if R is an equivalence relation, which does not mean restriction in biological and chemical applications.
  53.128 +
  53.129 +\subsection{Common problems}\label{sec:CommProb}
  53.130 +
  53.131 +The focus of this paper is on two extensively studied topics, the subgraph isomorphism and its variations. However, the following problems also appear in many applications.
  53.132 +
  53.133 +The \textbf{subgraph matching problem} is the following: is $G_{small}$ isomorphic to any subgraph of $G_{large}$ by a given node label?
  53.134 +
  53.135 +The \textbf{induced subgraph matching problem} asks the same about the existence of an induced subgraph.
  53.136 +
  53.137 +The \textbf{graph isomorphism problem} can be defined as induced subgraph matching problem where the sizes of the two graphs are equal.
  53.138 +
  53.139 +In addition to existence, it may be needed to show such a subgraph, or it may be necessary to list all of them.
  53.140 +
  53.141 +It should be noted that some authors misleadingly refer to the term \emph{subgraph isomorphism problem} as an \emph{induced subgraph isomorphism problem}.
  53.142 +
  53.143 +The following sections give the descriptions of VF2, VF2++, VF2 Plus and a particular comparison.
  53.144 +
  53.145 +\section{The VF2 Algorithm}
  53.146 +This algorithm is the basis of both the VF2++ and the VF2 Plus.
  53.147 +VF2 is able to handle all the variations mentioned in \textbf{Section \ref{sec:CommProb})}.
  53.148 +Although it can also handle directed graphs, for the sake of simplicity, only the undirected case will be discussed.
  53.149 +
  53.150 +
  53.151 +\subsection{Common notations}
  53.152 +\indent
  53.153 +Assume $G_{small}$ is searched in $G_{large}$.
  53.154 +The following definitions and notations will be used throughout the whole paper.
  53.155 +\begin{definition}
  53.156 +A set $M\subseteq V_{small}\times V_{large}$ is called \textbf{mapping}, if no node of $V_{small}$ or of $V_{large}$ appears in more than one pair in M.
  53.157 +That is, M uniquely associates some of the nodes in $V_{small}$ with some nodes of $V_{large}$ and vice versa.
  53.158 +\end{definition}
  53.159 +
  53.160 +\begin{definition}
  53.161 +Mapping M \textbf{covers} a node v, if there exists a pair in M, which contains v.
  53.162 +\end{definition}
  53.163 +
  53.164 +\begin{definition}
  53.165 +A mapping $M$ is $\mathbf{whole\ mapping}$, if $M$ covers all the nodes in $V_{small}$.
  53.166 +\end{definition}
  53.167 +
  53.168 +\begin{notation}
  53.169 +Let $\mathbf{M_{small}(s)} := \{u\in V_{small} : \exists v\in V_{large}: (u,v)\in M(s)\}$ and $\mathbf{M_{large}(s)} := \{v\in V_{large} : \exists u\in V_{small}: (u,v)\in M(s)\}$.
  53.170 +\end{notation}
  53.171 +
  53.172 +\begin{notation}
  53.173 +Let $\mathbf{Pair(M,v)}$ be the pair of $v$ in $M$, if such a node exist, otherwise $\mathbf{Pair(M,v)}$ is undefined. For a mapping $M$ and $v\in V_{small}\cup V_{large}$.
  53.174 +\end{notation}
  53.175 +
  53.176 +Note that if $\mathbf{Pair(M,v)}$ exists, then it is unique
  53.177 +
  53.178 +The definitions of the isomorphism types can be rephrased on the existence of a special whole mapping $M$, since it represents a bijection. For example 
  53.179 +\begin{center}
  53.180 +$M\subseteq V_{small}\times V_{large}$ represents an induced subgraph isomorphism $\Leftrightarrow$ $M$ is whole mapping and $\forall u,v \in{V_{small}} : (u,v)\in{E_{small}} \Leftrightarrow (Pair(M,u),Pair(M,v))\in E_{large}$.
  53.181 +\end{center}
  53.182 +
  53.183 +\begin{definition}
  53.184 +A set of whole mappings is called \textbf{problem type}.
  53.185 +\end{definition}
  53.186 +Throughout the paper, $\mathbf{PT}$ denotes a generic problem type which can be substituted by any problem type.
  53.187 +
  53.188 +A whole mapping $W\mathbf{\ is\ of\ type\ PT}$, if $W\in PT$. Using this notations, VF2 searches a whole mapping $W$ of type $PT$.
  53.189 +
  53.190 +For example the problem type of graph isomorphism problem is the following.
  53.191 +A whole mapping $W$ is in $\mathbf{ISO}$, iff the bijection represented by $W$ satisfies \textbf{Definition \ref{sec:ismorphic})}.
  53.192 +The subgraph- and induced subgraph matching problems can be formalized in a similar way. Let their problem types be denoted as $\mathbf{SUB}$ and $\mathbf{IND}$.
  53.193 +
  53.194 +\begin{definition}
  53.195 +\label{expPT}
  53.196 +$PT$ is an \textbf{expanding problem type} if $\ \forall\ W\in PT:\ \forall u_1,u_2\in V_{small}:\ (u_1,u_2)\in E_{small}\Rightarrow (Pair(W,u_1),Pair(W,u_2))\in E_{large}$, that is each edge of $G_{small}$ has to be mapped to an edge of $G_{large}$ for each mapping in $PT$.
  53.197 +\end{definition}
  53.198 +
  53.199 +Note that $ISO$, $SUB$ and $IND$ are expanding problem types.
  53.200 +
  53.201 +This paper deals with the three problem types mentioned above only, but
  53.202 +the following generic definitions make it possible to handle other types as well.
  53.203 +Although it may be challenging to find a proper consistency function and an efficient
  53.204 +cutting function.
  53.205 +
  53.206 +\begin{definition}
  53.207 +Let M be a mapping. A logical function $\mathbf{Cons_{PT}}$ is a \textbf{consistency function by } $\mathbf{PT}$, if the following holds. If there exists whole mapping $W$ of type PT for which $M\subseteq W$, then $Cons_{PT}(M)$ is true.
  53.208 +\end{definition}
  53.209 +
  53.210 +\begin{definition} 
  53.211 +Let M be a mapping. A logical function $\mathbf{Cut_{PT}}$ is a \textbf{cutting function by } $\mathbf{PT}$, if the following holds. $\mathbf{Cut_{PT}(M)}$ is false if $M$ can be extended to a whole mapping W of type PT.
  53.212 +\end{definition}
  53.213 +
  53.214 +\begin{definition}
  53.215 +$M$ is said to be \textbf{consistent mapping by} $\mathbf{PT}$, if $Cons_{PT}(M)$ is true. 
  53.216 +\end{definition}
  53.217 +
  53.218 +$Cons_{PT}$ and $Cut_{PT}$ will often be used in the following form.
  53.219 +\begin{notation}
  53.220 +Let $\mathbf{Cons_{PT}(p, M)}:=Cons_{PT}(M\cup\{p\})$ and $\mathbf{Cut_{PT}(p, M)}:=Cut_{PT}(M\cup\{p\})$, where $p\in{V_{small}\!\times\!V_{large}}$ and $M\cup\{p\}$ is mapping.
  53.221 +\end{notation}
  53.222 +
  53.223 +$Cons_{PT}$ will be used to check the consistency of the already covered nodes, while $Cut_{PT}$ is for looking ahead to recognize if no whole consistent mapping can contain the current mapping.
  53.224 +
  53.225 +\subsection{Overview of the algorithm}
  53.226 +VF2 uses a state space representation of mappings, $Cons_{PT}$ for excluding inconsistency with the problem type and $Cut_{PT}$ for pruning the search tree.
  53.227 +Each state $s$ of the matching process can be associated with a mapping $M(s)$.
  53.228 +
  53.229 +\textbf{Algorithm~\ref{alg:VF2Pseu})} is a high level description of the VF2 matching algorithm.
  53.230 +
  53.231 +
  53.232 +\begin{algorithm}
  53.233 +\algtext*{EndIf}%ne nyomtasson end if-et
  53.234 +\algtext*{EndFor}%ne nyomtasson ..
  53.235 +\algtext*{EndProcedure}%ne nyomtasson ..
  53.236 +\caption{\hspace{0.5cm}$A\ high\ level\ description\ of\ VF2$}\label{alg:VF2Pseu}
  53.237 +\begin{algorithmic}[1]
  53.238 +
  53.239 +\Procedure{VF2}{State $s$, ProblemType $PT$}
  53.240 +  \If{$M(s$) covers $V_{small}$}
  53.241 +    \State Output($M(s)$)
  53.242 +  \Else
  53.243 +  
  53.244 +  \State Compute the set $P(s)$ of the pairs candidate for inclusion in $M(s)$
  53.245 +  \ForAll{$p\in{P(s)}$}
  53.246 +    \If{Cons$_{PT}$($p, M(s)$) $\wedge$ $\neg$Cut$_{PT}$($p, M(s)$)}
  53.247 +      \State Compute the nascent state $\tilde{s}$ by adding $p$ to $M(s)$
  53.248 +      \State \textbf{call} VF2($\tilde{s}$, $PT$)
  53.249 +    \EndIf
  53.250 +  \EndFor
  53.251 +  \EndIf
  53.252 +\EndProcedure
  53.253 +\end{algorithmic}
  53.254 +\end{algorithm}
  53.255 +
  53.256 +
  53.257 +The initial state $s_0$ is associated with $M(s_0)=\emptyset$, i.e. it starts with an empty mapping.
  53.258 +
  53.259 +For each state $s$, the algorithm computes $P(s)$, the set of candidate node pairs for adding to the current state $s$.
  53.260 +
  53.261 +For each pair $p$ in $P(s)$, $Cons_{PT}(p,M(s))$ and $Cut_{PT}(p,M(s))$ are evaluated. If $Cons_{PT}(p,M(s))$ is true and $Cut_{PT}(p,M(s))$ is false, the successor state $\tilde{s}=s\cup \{p\}$ is computed, and the whole process is recursively applied to $\tilde{s}$. Otherwise, $\tilde{s}$ is not consistent by $PT$ or it can be proved that $s$ can not be extended to a whole mapping.
  53.262 +
  53.263 +In order to make sure of the correctness see
  53.264 +\begin{claim}
  53.265 +Through consistent mappings, only consistent whole mappings can be reached, and all of the whole mappings are reachable through consistent mappings.
  53.266 +\end{claim}
  53.267 +
  53.268 +Note that a state may be reached in many different ways, since the order of insertions into M does not influence the nascent mapping. In fact, the number of different ways which lead to the same state can be exponentially large. If $G_{small}$ and $G_{large}$ are circles with n nodes and n different node labels, there exists exactly one graph isomorphism between them, but it will be reached in $n!$ different ways.
  53.269 +
  53.270 +However, one may observe
  53.271 +
  53.272 +\begin{claim}
  53.273 +\label{claim:claimTotOrd}
  53.274 +Let $\prec$ an arbitrary total ordering relation on $V_{small}$.
  53.275 +If the algorithm ignores each $p=(u,v) \in P(s)$, for which
  53.276 +\begin{center}
  53.277 +$\exists (\hat{u},\hat{v})\in P(s): \hat{u} \prec u$,
  53.278 +\end{center}
  53.279 +then no state can be reached more than ones and each state associated with a whole mapping remains reachable. 
  53.280 +\end{claim}
  53.281 +
  53.282 +Note that the cornerstone of the improvements to VF2 is a proper choice of a total ordering.
  53.283 +
  53.284 +\subsection{The candidate set P(s)}
  53.285 +\label{candidateComputingVF2}
  53.286 +$P(s)$ is the set of the candidate pairs for inclusion in $M(s)$.
  53.287 +Suppose that $PT$ is an expanding problem type, see \textbf{Definition~\ref{expPT})}.
  53.288 +
  53.289 +\begin{notation}
  53.290 +Let $\mathbf{T_{small}(s)}:=\{u \in V_{small} : u$ is not covered by $M(s)\wedge\exists \tilde{u}\in{V_{small}: (u,\tilde{u})\in E_{small}} \wedge \tilde{u}$ is covered by $M(s)\}$, and \\ $\mathbf{T_{large}(s)}\!:=\!\{v \in\!V_{large}\!:\!v$ is not covered by $M(s)\wedge\!\exists\tilde{v}\!\in\!{V_{large}\!:\!(v,\tilde{v})\in\!E_{large}} \wedge \tilde{v}$ is covered by $M(s)\}$
  53.291 +\end{notation}
  53.292 +
  53.293 +The set $P(s)$ includes the pairs of uncovered neighbours of covered nodes and if there is not such a node pair, all the pairs containing two uncovered nodes are added. Formally, let
  53.294 +\[
  53.295 + P(s)\!=\!
  53.296 +  \begin{cases} 
  53.297 +   T_{small}(s)\times T_{large}(s)&\hspace{-0.15cm}\text{if } T_{small}(s)\!\neq\!\emptyset\!\wedge\!T_{large}(s)\!\neq \emptyset,\\
  53.298 +   (V_{small}\!\setminus\!M_{small}(s))\!\times\!(V_{large}\!\setminus\!M_{large}(s)) &\hspace{-0.15cm}otherwise.
  53.299 +  \end{cases}
  53.300 +\]
  53.301 +
  53.302 +\subsection{Consistency}
  53.303 +This section defines the consistency functions for the different problem types mentioned in \textbf{Section \ref{sec:CommProb})}.
  53.304 +\begin{notation}
  53.305 +Let $\mathbf{\Gamma_{small} (u)}:=\{\tilde{u}\in V_{small} : (u,\tilde{u})\in E_{small}\}$\\
  53.306 +Let $\mathbf{\Gamma_{large} (v)}:=\{\tilde{v}\in V_{large} : (v,\tilde{v})\in E_{large}\}$
  53.307 +\end{notation}
  53.308 +Suppose $p=(u,v)$, where $u\in V_{small}$ and $v\in V_{large}$,
  53.309 +$s$ is a state of the matching procedure,
  53.310 +$M(s)$ is consistent mapping by $PT$ and $lab(u)=lab(v)$.
  53.311 +$Cons_{PT}(p,M(s))$ checks whether including pair $p$ into $M(s)$ leads to a consistent mapping by $PT$.
  53.312 +
  53.313 +\subsubsection{Induced subgraph isomorphism}
  53.314 +$M(s)\cup \{(u,v)\}$ is a consistent mapping by $IND$ $\Leftrightarrow (\forall \tilde{u}\in M_{small}: (u,\tilde{u})\in E_{small} \Leftrightarrow (v,Pair(M(s),\tilde{u}))\in E_{large})$.\newline
  53.315 +The following formulation gives an efficient way of calculating $Cons_{IND}$.
  53.316 +\begin{claim}
  53.317 +$Cons_{IND}((u,v),M(s)):=(\forall \tilde{v}\in \Gamma_{large}(v) \ \cap\ M_{large}(s):\\(Pair(M(s),\tilde{v}),u)\in E_{small})\wedge 
  53.318 +(\forall \tilde{u}\in \Gamma_{small}(u) \ \cap\ M_{small}(s):(v,Pair(M(s),\tilde{u}))\in E_{large})$ is a consistency function in the case of $IND$.
  53.319 +\end{claim}
  53.320 +
  53.321 +\subsubsection{Graph isomorphism}
  53.322 +$M(s)\cup \{(u,v)\}$ is a consistent mapping by $ISO$ $\Leftrightarrow$  $M(s)\cup \{(u,v)\}$ is a consistent mapping by $IND$.
  53.323 +\begin{claim}
  53.324 +$Cons_{ISO}((u,v),M(s))$ is a consistency function by $ISO$ if and only if it is a consistency function by $IND$.
  53.325 +\end{claim}
  53.326 +\subsubsection{Subgraph isomorphism}
  53.327 +$M(s)\cup \{(u,v)\}$ is a consistent mapping by $SUB$ $\Leftrightarrow (\forall \tilde{u}\in M_{small}:\\(u,\tilde{u})\in E_{small} \Rightarrow (v,Pair(M(s),\tilde{u}))\in E_{large})$.
  53.328 +\newline
  53.329 +The following formulation gives an efficient way of calculating $Cons_{SUB}$.
  53.330 +\begin{claim}
  53.331 +$Cons_{SUB}((u,v),M(s)):=
  53.332 +(\forall \tilde{u}\in \Gamma_{small}(u) \ \cap\ M_{small}(s):\\(v,Pair(M(s),\tilde{u}))\in E_{large})$ is a consistency function by $SUB$.
  53.333 +\end{claim}
  53.334 +
  53.335 +\subsection{Cutting rules}
  53.336 +$Cut_{PT}(p,M(s))$ is defined by a collection of efficiently verifiable conditions. The requirement is that $Cut_{PT}(p,M(s))$ can be true only if it is impossible to extended $M(s)\cup \{p\}$ to a whole mapping.
  53.337 +\begin{notation}
  53.338 +
  53.339 +Let $\mathbf{\tilde{T}_{small}}(s):=(V_{small}\backslash M_{small}(s))\backslash T_{small}(s)$, and \\ $\mathbf{\tilde{T}_{large}}(s):=(V_{large}\backslash M_{large}(s))\backslash T_{large}(s)$.
  53.340 +\end{notation}
  53.341 +\subsubsection{Induced subgraph isomorphism}
  53.342 +\begin{claim}
  53.343 +$Cut_{IND}((u,v),M(s)):= |\Gamma_{large} (v)\ \cap\ T_{large}(s)| < |\Gamma_{small} (u)\ \cap\ T_{small}(s)| \vee |\Gamma_{large}(v)\cap \tilde{T}_{large}(s)| < |\Gamma_{small}(u)\cap \tilde{T}_{small}(s)|$ is a cutting function by $IND$.
  53.344 +\end{claim}
  53.345 +\subsubsection{Graph isomorphism}
  53.346 +Note that the cutting function of induced subgraph isomorphism defined above is a cutting function by $ISO$, too, however it is less efficient than the following while their computational complexity is the same.
  53.347 +\begin{claim}
  53.348 +$Cut_{ISO}((u,v),M(s)):= |\Gamma_{large} (v)\ \cap\ T_{large}(s)| \neq |\Gamma_{small} (u)\ \cap\ T_{small}(s)| \vee |\Gamma_{large}(v)\cap  \tilde{T}_{large}(s)| \neq |\Gamma_{small}(u)\cap \tilde{T}_{small}(s)|$ is a cutting function by $ISO$.
  53.349 +\end{claim}
  53.350 +
  53.351 +\subsubsection{Subgraph isomorphism}
  53.352 +\begin{claim}
  53.353 +$Cut_{SUB}((u,v),M(s)):= |\Gamma_{large} (v)\ \cap\ T_{large}(s)| < |\Gamma_{small} (u)\ \cap\ T_{small}(s)|$ is a cutting function by $SUB$.
  53.354 +\end{claim}
  53.355 +Note that there is a significant difference between induced and non-induced subgraph isomorphism:
  53.356 +
  53.357 +\begin{claim}
  53.358 +\label{claimSUB}
  53.359 +$Cut_{SUB}'((u,v),M(s)):= |\Gamma_{large} (v)\ \cap\ T_{large}(s)| < |\Gamma_{small} (u)\ \cap\ T_{small}(s)| \vee |\Gamma_{large}(v)\cap \tilde{T}_{large}(s)| < |\Gamma_{small}(u)\cap \tilde{T}_{small}(s)|$ is \textbf{not} a cutting function by $SUB$.
  53.360 +\end{claim}
  53.361 +\begin{proof}$ $\\
  53.362 +\vspace*{-0.5cm}
  53.363 +
  53.364 +\begin{figure}
  53.365 +\begin{center}
  53.366 +\begin{tikzpicture}
  53.367 +  [scale=.8,auto=left,every node/.style={circle,fill=black!15}]
  53.368 +  \node[rectangle,fill=black!15] at (4,6) {$G_{small}$};
  53.369 +  \node (u4) at (2.5,10)  {$u_4$};
  53.370 +  \node (u3) at (5.5,10) {$u_3$};
  53.371 +  \node (u1) at (2.5,7)  {$u_1$};
  53.372 +  \node (u2) at (5.5,7) {$u_2$};
  53.373 +  
  53.374 +  \node[rectangle,fill=black!30] at (13.5,6) {$G_{large}$};
  53.375 +  \node[fill=black!30] (v4) at (12,10)  {$v_4$};
  53.376 +  \node[fill=black!30] (v3) at (15,10) {$v_3$};
  53.377 +  \node[fill=black!30] (v1) at (12,7)  {$v_1$};
  53.378 +  \node[fill=black!30] (v2) at (15,7) {$v_2$};
  53.379 +  
  53.380 +
  53.381 +  \foreach \from/\to in {u1/u2,u2/u3,u3/u4,u4/u1}
  53.382 +    \draw (\from) -- (\to);
  53.383 +  \foreach \from/\to in {v1/v2,v2/v3,v3/v4,v4/v1,v1/v3}
  53.384 +    \draw (\from) -- (\to);
  53.385 +%    \draw[dashed] (\from) -- (\to);
  53.386 +\end{tikzpicture}
  53.387 +\caption{Graphs for the proof of \textbf{Claim \ref{claimSUB}}} \label{fig:proofSUB}
  53.388 +\end{center}
  53.389 +\end{figure}
  53.390 +Let the two graphs of \textbf{Figure \ref{fig:proofSUB})} be the input graphs.
  53.391 +Suppose the total ordering relation is $u_1 \prec u_2 \prec u_3 \prec u_4$,$M(s)\!=\{(u_1,v_1)\}$, and VF2 tries to add $(u_2,v_2)\in P(s)$.\newline
  53.392 +$Cons_{SUB}((u_2,v_2),M(s))=true$, so $M\cup \{(u_2,v_2)\}$ is consistent by $SUB$. The cutting function $Cut_{SUB}((u_2,v_2),M(s))$ is false, so it does not let cut the tree.\newline
  53.393 +On the other hand $Cut_{SUB}'((u_2,v_2),M(s))$ is true, since\\$0=|\Gamma_{large}(v_2)\cap \tilde{T}_{large}(s)|<|\Gamma_{small}(u_2)\cap \tilde{T}_{small}(s)|=1$ is true, but still the tree can not be pruned, because otherwise the $\{(u_1,v_1)(u_2,v_2)(u_3,v_3)(u_4,v_4)\}$ mapping can not be found.
  53.394 +\end{proof}
  53.395 +
  53.396 +\newpage
  53.397 +\section{The VF2++ Algorithm}
  53.398 +Although any total ordering relation makes the search space of VF2 a tree, its
  53.399 +choice turns out to dramatically influence the number of visited states. The goal is to determine an efficient one as quickly as possible.
  53.400 +
  53.401 +The main reason for VF2++' superiority over VF2 is twofold. Firstly, taking into account the structure and the node labeling of the graph, VF2++ determines a state order in which most of the unfruitful branches of the search space can be pruned immediately. Secondly, introducing more efficient --- nevertheless still easier to compute --- cutting rules reduces the chance of going astray even further.
  53.402 +
  53.403 +In addition to the usual subgraph isomorphism, specialized versions for induced subgraph isomorphism and for graph isomorphism have been designed. VF2++ has gained a runtime improvement of one order of magnitude respecting induced subgraph isomorphism and a better asymptotical behaviour in the case of graph isomorphism problem.
  53.404 +
  53.405 +Note that a weaker version of the cutting rules and the more efficient candidate
  53.406 +set calculating were described in \cite{VF2Plus}, too.
  53.407 +
  53.408 +It should be noted that all the methods described in this section are extendable to handle directed graphs and edge labels as well.
  53.409 +
  53.410 +The basic ideas and the detailed description of VF2++ are provided in the following.
  53.411 +
  53.412 +\subsection{Preparations}
  53.413 +\begin{claim}
  53.414 +\label{claim:claimCoverFromLeft}
  53.415 +The total ordering relation uniquely determines a node order, in which the nodes of $V_{small}$ will be covered by VF2. From the point of view of the matching procedure, this means, that always the same node of $G_{small}$ will be covered on the d-th level.
  53.416 +\end{claim}
  53.417 +\begin{proof}
  53.418 +In order to make the search space a tree, the pairs in $\{(u,v)\in P(s) : \exists \hat{u} : \hat{u}\prec u\}$ are excluded from $P(s)$.
  53.419 +\newline
  53.420 +Let $\tilde{P}(s):=P(s)\backslash \{(u,v)\in P(s) : \exists \hat{u} : \hat{u}\prec u\}$
  53.421 +\newline
  53.422 +The relation $\prec$ is a total ordering, so $\exists!\ \tilde{u} : \forall\ (u,v)\in \tilde{P}(s): u=\tilde u$. Since a pair form $\tilde{P}(s)$ is chosen for including into $M(s)$, it is obvious, that only $\tilde{u}$ can be covered in $V_{small}$. Actually, $\tilde{u}$ is the smallest element in $T_{small}(s)$ (or in $V_{small}\backslash M_{small}(s)$, if $T_{small}(s)$ were empty), and $T_{small}(s)$ depends only on the covered nodes of $G_{small}$. 
  53.423 +\newline
  53.424 +Simple induction on $d$ shows that the set of covered nodes of $G_{small}$ is unique, if $d$ is given, so $\tilde{u}$ is unique if $d$ is given.
  53.425 +\end{proof}
  53.426 +
  53.427 +\begin{definition}
  53.428 +An order $(u_{\sigma(1)},u_{\sigma(2)},..,u_{\sigma(|V_{small}|)})$ of $V_{small}$ is \textbf{matching order}, if exists $\prec$ total ordering relation, s.t. the VF2 with $\prec$ on the d-th level finds pair for $u_{\sigma(d)}$ for all $d\in\{1,..,|V_{small}|\}$.
  53.429 +\end{definition}
  53.430 +
  53.431 +\begin{claim}\label{claim:MOclaim}
  53.432 +A total ordering is matching order, iff the nodes of every component form an interval in the node sequence, and every node connects to a previous node in its component except the first node of the component. The order of the components is arbitrary.
  53.433 +\\Formally spoken, an order $(u_{\sigma(1)},u_{\sigma(2)},..,u_{\sigma(|V_{small}|)})$ of $V_{small}$ is matching order $\Leftrightarrow$ $\forall G'_{small}=(V'_{small},E'_{small})\ component\ of\ G_{small}: \forall i: (\exists j : j<i\wedge u_{\sigma(j)},u_{\sigma(i)}\in V'_{small})\Rightarrow \exists k : k < i \wedge (\forall l: k\leq l\leq i \Rightarrow u_{l}\in V'_{small}) \wedge (u_{\sigma{(k)}},u_{\sigma{(i)}})\in E'_{small}$, where $i,j,k,l\in \{1,..,|V_{small}|\}$\newline
  53.434 +\end{claim}
  53.435 +\begin{proof}
  53.436 +Suppose a matching order is given. It has to be shown that the node sequence has a structure described above.\\
  53.437 +Let $G'_{small}=(V'_{small},E'_{small})$ be an arbitrary component and $i$ an arbitrary index. 
  53.438 +\newline
  53.439 +$(\exists j : j<i\wedge u_{\sigma(j)},u_{\sigma(i)}\in V'_{small})\Rightarrow u_{\sigma(i)}$ is not the first covered node in $G_{small}\ \Rightarrow u_{\sigma(i)}$ is connected to a covered node $u_{\sigma(k)}$ where $k<i$, since $u_{\sigma(i)}\in T_{small}(s)$ for some $s$ and $T_{small}(s)\subseteq{V'_{small}}$ contains only nodes connected to at least one covered node. It's easy to see, that $\forall l: k\leq l\leq i \Rightarrow u_{l}\in V'_{small}$, since $T_{small}(s)$ contains only nodes connected to some covered ones, while it is not empty, but if it were empty, then $u_{\sigma(k)}$ and $u_{\sigma(i)}$ were not in the same component.
  53.440 +
  53.441 +Now, let us show that if a node sequence has the special structure described above, it has to be matching order.\\ $(u_{\sigma(1)},u_{\sigma(2)},..,u_{\sigma(|V_{small}|)})$ is a total ordering, which determines the matching order $(u_{\sigma(1)},u_{\sigma(2)},..,u_{\sigma(|V_{small}|)})$.
  53.442 +\end{proof}
  53.443 +
  53.444 +To summing up, a total ordering always uniquely determines a matching order, and every matching order can be determined by a total ordering, however, more than one different total orderings may determine the same matching order.
  53.445 +\subsection{Idea behind the algorithm}
  53.446 +The goal is to find a matching order in which the algorithm is able to recognize inconsistency or prune the infeasible branches on the highest levels and goes deep only if it is needed.
  53.447 +
  53.448 +\begin{notation}
  53.449 +Let $\mathbf{Conn_{H}(u)}:=|\Gamma_{small}(u)\cap H\}|$, that is the number of neighbours of u which are in H, where $u\in V_{small} $ and $H\subseteq V_{small}$.
  53.450 +\end{notation}
  53.451 +
  53.452 +The principal question is the following. Suppose a state $s$ is given. For which node of $T_{small}(s)$ is the hardest to find a consistent pair in $G_{large}$? The more covered neighbours a node in $T_{small}(s)$ has --- i.e. the largest $Conn_{M_{small}(s)}$ it has ---, the more rarely satisfiable consistency constraints for its pair are given.
  53.453 +
  53.454 +In biology, most of the graphs are sparse, thus several nodes in $T_{small}(s)$ may have the same $Conn_{M_{small}(s)}$, which makes reasonable to define a secondary and a tertiary order between them.
  53.455 +The observation above proves itself to be as determining, that the secondary ordering prefers nodes with the most uncovered neighbours among which have the same $Conn_{M_{small}(s)}$ to increase $Conn_{M_{small}(s)}$ of uncovered nodes so much, as possible.
  53.456 +The tertiary ordering prefers nodes having the rarest uncovered labels.
  53.457 +
  53.458 +Note that the secondary ordering is the same as the ordering by $deg$, which is a static data in front of the above used.
  53.459 +
  53.460 +These rules can easily result in a matching order which contains the nodes of a long path successively, whose nodes may have low $Conn$ and is easily matchable into $G_{large}$. To avoid that, a BFS order is used, which provides the shortest possible paths.
  53.461 +\newline
  53.462 +
  53.463 +In the following, some examples on which the VF2 may be slow are described, although they are easily solvable by using a proper matching order.
  53.464 +
  53.465 +\begin{example}
  53.466 +Suppose $G_{small}$ can be mapped into $G_{large}$ in many ways without node labels. Let $u\in V_{small}$ and $v\in V_{large}$.
  53.467 +\newline
  53.468 +$lab(u):=black$
  53.469 +\newline
  53.470 +$lab(v):=black$
  53.471 +\newline
  53.472 +$lab(\tilde{u}):=red \  \forall \tilde{u}\in (V_{small}\backslash \{u\})$
  53.473 +\newline
  53.474 +$lab(\tilde{v}):=red \  \forall \tilde{v}\in (V_{large}\backslash \{v\})$
  53.475 +\newline
  53.476 +
  53.477 +Now, any mapping by the node label $lab$ must contain $(u,v)$, since $u$ is black and no node in $V_{large}$ has a black label except $v$. If unfortunately $u$ were the last node which will get covered, VF2 would check only in the last steps, whether $u$ can be matched to $v$.
  53.478 +\newline
  53.479 +However, had $u$ been the first matched node, u would have been matched immediately to v, so all the mappings would have been precluded in which node labels can not correspond.
  53.480 +\end{example}
  53.481 +
  53.482 +\begin{example}
  53.483 +Suppose there is no node label given, $G_{small}$ is a small graph and can not be mapped into $G_{large}$ and $u\in V_{small}$.
  53.484 +\newline
  53.485 +Let $G'_{small}:=(V_{small}\cup \{u'_{1},u'_{2},..,u'_{k}\},E_{small}\cup \{(u,u'_{1}),(u'_{1},u'_{2}),..,(u'_{k-1},u'_{k})\})$, that is, $G'_{small}$ is $G_{small}\cup \{ a\ k$ long path, which is disjoint from $G_{small}$ and one of its starting points is connected to $u\in V_{small}\}$.
  53.486 +\newline
  53.487 +Is there a subgraph of $G_{large}$, which is isomorph with $G'_{small}$?
  53.488 +\newline
  53.489 +If unfortunately the nodes of the path were the first $k$ nodes in the matching order, the algorithm would iterate through all the possible k long paths in $G_{large}$, and it would recognize that no path can be extended to $G'_{small}$.
  53.490 +\newline
  53.491 +However, had it started by the matching of $G_{small}$, it would not have matched any nodes of the path.
  53.492 +\end{example}
  53.493 +
  53.494 +These examples may look artificial, but the same problems also appear in real-world examples, even though in a less obvious way.
  53.495 +
  53.496 +\subsection{Total ordering}
  53.497 +Instead of the total ordering relation, the matching order will be searched directly.
  53.498 +\begin{notation}
  53.499 +Let \textbf{F$_\mathcal{M}$(l)}$:=|\{v\in V_{large} : l=lab(v)\}|-|\{u\in V_{small}\backslash \mathcal{M} : l=lab(u)\}|$ , where $l$ is a label and $\mathcal{M}\subseteq V_{small}$.
  53.500 +\end{notation}
  53.501 +
  53.502 +\begin{definition}Let $\mathbf{arg\ max}_{f}(S) :=\{u : u\in S \wedge f(u)=max_{v\in S}\{f(v)\}\}$ and $\mathbf{arg\ min}_{f}(S) := arg\ max_{-f}(S)$, where $S$ is a finite set and $f:S\longrightarrow \mathbb{R}$.
  53.503 +\end{definition}
  53.504 +
  53.505 +\begin{algorithm}
  53.506 +\algtext*{EndIf}%ne nyomtasson end if-et
  53.507 +\algtext*{EndFor}%ne nyomtasson ..
  53.508 +\algtext*{EndProcedure}%ne nyomtasson ..
  53.509 +\algtext*{EndWhile}
  53.510 +\caption{\hspace{0.5cm}$The\ method\ of\ VF2++\ for\ determining\ the\ node\ order$}\label{alg:VF2PPPseu}
  53.511 +\begin{algorithmic}[1]
  53.512 +\Procedure{VF2++order}{}
  53.513 +  \State $\mathcal{M}$ := $\emptyset$ \Comment{matching order}
  53.514 +  \While{$V_{small}\backslash \mathcal{M} \neq\emptyset$}
  53.515 +  \State $r\in$ arg max$_{deg}$ (arg min$_{F_\mathcal{M}\circ lab}(V_{small}\backslash \mathcal{M})$)\label{alg:findMin}
  53.516 +  \State Compute $T$, a BFS tree with root node $r$.
  53.517 +  \For{$d=0,1,...,depth(T)$}
  53.518 +  \State $V_d$:=nodes of the $d$-th level
  53.519 +  \State Process $V_d$ \Comment{See Algorithm \ref{alg:VF2PPProcess1}) and \ref{alg:VF2PPProcess2})}
  53.520 +  \EndFor
  53.521 +  \EndWhile
  53.522 +\EndProcedure
  53.523 +\end{algorithmic}
  53.524 +\end{algorithm}
  53.525 +
  53.526 +\begin{algorithm}
  53.527 +\algtext*{EndIf}%ne nyomtasson end if-et
  53.528 +\algtext*{EndFor}%ne nyomtasson ..
  53.529 +\algtext*{EndProcedure}%ne nyomtasson ..
  53.530 +\algtext*{EndWhile}
  53.531 +\caption{\hspace{.5cm}$A\ method\ for\ processing\ a\ level\ of\ the\ BFS\ tree$}\label{alg:VF2PPProcess1}
  53.532 +\begin{algorithmic}[1]
  53.533 +\Procedure{VF2++ProcessLevel1}{$V_{d}$}
  53.534 +  \While{$V_d\neq\emptyset$}
  53.535 +  \State $m\in$ arg min$_{F_\mathcal{M}\circ\ lab}($ arg max$_{deg}($arg max$_{Conn_{\mathcal{M}}}(V_{d})))$
  53.536 +  \State $V_d:=V_d\backslash m$
  53.537 +  \State Append node $m$ to the end of $\mathcal{M}$
  53.538 +  \State Refresh $F_\mathcal{M}$
  53.539 +  \EndWhile
  53.540 +\EndProcedure
  53.541 +\end{algorithmic}
  53.542 +\end{algorithm}
  53.543 +
  53.544 +\begin{algorithm}
  53.545 +\algtext*{EndIf}%ne nyomtasson end if-et
  53.546 +\algtext*{EndFor}%ne nyomtasson ..
  53.547 +\algtext*{EndProcedure}%ne nyomtasson ..
  53.548 +\algtext*{EndWhile}
  53.549 +\caption{\hspace{0.5cm}$Another\ method\ for\ processing\ a\ level\ of\ the\ BFS\ tree$}\label{alg:VF2PPProcess2}
  53.550 +\begin{algorithmic}[1]
  53.551 +\Procedure{VF2++ProcessLevel2}{$V_{d}$}
  53.552 +  \State Sort $V_d$ in descending lex. order by $(Conn_{\mathcal{M}},deg,-F_\mathcal{M})$
  53.553 +  \State Append the sorted $V_d$ to the end of $\mathcal{M}$
  53.554 +  \State Refresh $F_\mathcal{M}$
  53.555 +\EndProcedure
  53.556 +\end{algorithmic}
  53.557 +\end{algorithm}
  53.558 +\textbf{Algorithm~\ref{alg:VF2PPPseu})} is a high level description of the matching order procedure of VF2++. It computes a BFS tree for each component in ascending order of their rarest $lab$ and largest $deg$, whose root vertex is the component's minimal node. \textbf{Algorithm \ref{alg:VF2PPProcess1})} and \textbf{\ref{alg:VF2PPProcess2})} are two different methods to process a level of the BFS tree.
  53.559 +
  53.560 +After sorting the nodes of the current level in descending lexicographic order by $(Conn_{\mathcal{M}},deg,-F_\mathcal{M})$, \textbf{Algorithm \ref{alg:VF2PPProcess2})} appends them simultaneously to the matching order $\mathcal{M}$ and refreshes $F_\mathcal{M}$ just once, whereas \textbf{Algorithm \ref{alg:VF2PPProcess1})} appends the nodes separately to $\mathcal{M}$ and refreshes $F_\mathcal{M}$ immediately, so it provides up-to-date label information and may result in a more efficient matching order.
  53.561 +
  53.562 +\textbf{Claim~\ref{claim:MOclaim})} shows that \textbf{Algorithm \ref{alg:VF2PPPseu})} provides a matching order.
  53.563 +
  53.564 +
  53.565 +\subsection{Cutting rules}
  53.566 +\label{VF2PPCuttingRules}
  53.567 +This section presents the cutting rules of VF2++, which are improved by using extra information coming from the node labels.
  53.568 +\begin{notation}
  53.569 +Let $\mathbf{\Gamma_{small}^{l}(u)}:=\{\tilde{u} : lab(\tilde{u})=l \wedge \tilde{u}\in \Gamma_{small} (u)\}$ and $\mathbf{\Gamma_{large}^{l}(v)}:=\{\tilde{v} : lab(\tilde{v})=l \wedge \tilde{v}\in \Gamma_{large} (v)\}$, where $u\in V_{small}$, $v\in V_{large}$ and $l$ is a label.
  53.570 +\end{notation}
  53.571 +
  53.572 +\subsubsection{Induced subgraph isomorphism}
  53.573 +\begin{claim}
  53.574 +\[LabCut_{IND}((u,v),M(s))\!:=\!\!\!\!\!\bigvee_{l\ is\ label}\!\!\!\!\!\!\!|\Gamma_{large}^{l} (v) \cap T_{large}(s)|\!<\!|\Gamma_{small}^{l}(u)\cap T_{small}(s)|\ \vee\]\[\bigvee_{l\ is\ label} \newline |\Gamma_{large}^{l}(v)\cap \tilde{T}_{large}(s)| < |\Gamma_{small}^{l}(u)\cap \tilde{T}_{small}(s)|\] is a cutting function by IND.
  53.575 +\end{claim}
  53.576 +\begin{proof}
  53.577 +It has to be shown, that $LabCut_{IND}((u,v),M(s))=true\Rightarrow$ the mapping can not be extended to a whole mapping.\\
  53.578 +$LabCut_{IND}((u,v),M(s))=true,$ iff the following holds. $\\\exists l: |\Gamma_{large}^{l} (v)\ \cap\ T_{large}(s)| < |\Gamma_{small}^{l} (u)\ \cap\ T_{small}(s)| \vee |\Gamma_{large}^{l}(v)\cap \tilde{T}_{large}(s)| < |\Gamma_{small}^{l}(u)\cap \tilde{T}_{small}(s)|$.
  53.579 +
  53.580 +Suppose that $|\Gamma_{large}^{l} (v)\ \cap\ T_{large}(s)| < |\Gamma_{small}^{l} (u)\ \cap\ T_{small}(s)|$. Each node of $\Gamma_{small}^{l} (u)\ \cap\ T_{small}(s)$ has to be matched to a node in $\Gamma_{large}^{l} (v)\ \cap\ T_{large}(s)$, so $\Gamma_{large}^{l} (v)\ \cap\ T_{large}(s)$ can not be smaller than $\Gamma_{small}^{l} (u)\ \cap\ T_{small}(s)$. That is why $M(s)$ can not be extended to a whole mapping.
  53.581 +
  53.582 +Otherwise $|\Gamma_{large}^{l}(v)\cap \tilde{T}_{large}(s)| < |\Gamma_{small}^{l}(u)\cap \tilde{T}_{small}(s)|$ has to be true. Similarly, each node of $\Gamma_{large}^{l}(v)\cap \tilde{T}_{large}(s)$ has to be matched to a node in $\Gamma_{small}^{l}(u)\cap \tilde{T}_{small}(s)$, i.e. $\Gamma_{large}^{l}(v)\cap \tilde{T}_{large}(s)$ can not be smaller than $\Gamma_{small}^{l}(u)\cap \tilde{T}_{small}(s)$, if $M(s)$ is extendible.
  53.583 +\end{proof}
  53.584 +The following claims can be proven similarly.
  53.585 +\subsubsection{Graph isomorphism}
  53.586 +\begin{claim}
  53.587 +\[LabCut_{ISO}((u,v),M(s))\!:=\!\!\!\!\!\bigvee_{l\ is\ label}\!\!\!\!\!\!\!|\Gamma_{large}^{l} (v) \cap T_{large}(s)|\!\neq\!|\Gamma_{small}^{l}(u)\cap T_{small}(s)|\  \vee\]\[\bigvee_{l\ is\ label} \newline |\Gamma_{large}^{l}(v)\cap \tilde{T}_{large}(s)| \neq |\Gamma_{small}^{l}(u)\cap \tilde{T}_{small}(s)|\] is a cutting function by ISO.
  53.588 +\end{claim}
  53.589 +
  53.590 +\subsubsection{Subgraph isomorphism}
  53.591 +\begin{claim}
  53.592 +\[LabCut_{IND}((u,v),M(s))\!:=\!\!\!\!\!\bigvee_{l\ is\ label}\!\!\!\!\!\!\!|\Gamma_{large}^{l} (v) \cap T_{large}(s)|\!<\!|\Gamma_{small}^{l}(u)\cap T_{small}(s)|\] is a cutting function by SUB.
  53.593 +\end{claim}
  53.594 +
  53.595 +
  53.596 +
  53.597 +\subsection{Implementation details}
  53.598 +This section provides a detailed summary of an efficient implementation of VF2++.
  53.599 +\subsubsection{Storing a mapping}
  53.600 +After fixing an arbitrary node order ($u_0, u_1, .., u_{|G_{small}|-1}$) of $G_{small}$, an array $M$ is usable to store the current mapping in the following way.
  53.601 +\[
  53.602 + M[i] = 
  53.603 +  \begin{cases} 
  53.604 +   v & if\ (u_i,v)\ is\ in\ the\ mapping\\
  53.605 +   INVALID & if\ no\ node\ has\ been\ mapped\ to\ u_i.
  53.606 +  \end{cases}
  53.607 +\]
  53.608 +Where $i\in\{0,1, ..,|G_{small}|-1\}$, $v\in V_{large}$ and $INVALID$ means "no node".
  53.609 +\subsubsection{Avoiding the recurrence}
  53.610 +Exploring the state space was described in a recursive fashion using sets (see \textbf{Algorithm~\ref{alg:VF2Pseu})}), which makes the algorithm easy to understand but does not show directly an efficient way of implementation. The following approach avoiding recursion and using lookup tables instead of sets is not only fast but has linear space complexity as well.
  53.611 +
  53.612 +The recursion of \textbf{Algorithm~\ref{alg:VF2Pseu})} can be realized as a while loop, which has a loop counter $depth$ denoting the all-time depth of the recursion.
  53.613 +Fixing a matching order, let $M$ denote the array storing the all-time mapping.
  53.614 +The initial state is associated with the empty mapping, which means that $\forall i: M[i]=INVALID$ and $depth=0$.
  53.615 +In case of a recursive call, $depth$ has to be incremented, while in case of a return, it has to be decremented.
  53.616 +Based on \textbf{Claim~\ref{claim:claimCoverFromLeft})}, $M$ is $INVALID$ from index $depth$+1 and not $INVALID$ before $depth$, i.e. $\forall i: i < depth \Rightarrow M[i]\neq INVALID$ and $\forall i: i > depth \Rightarrow M[i]= INVALID$. $M[depth]$ changes while the state is being processed, but the property is held before both stepping back to a predecessor state and exploring a successor state.
  53.617 +
  53.618 +The necessary part of the candidate set is easily maintainable or computable by following \textbf{Section~\ref{candidateComputingVF2})}. A much faster method has been designed for biological- and sparse graphs, see the next section for details.
  53.619 +
  53.620 +\subsubsection{Calculating the candidates for a node}
  53.621 +Being aware of \textbf{Claim~\ref{claim:claimCoverFromLeft})}, the task is not to maintain the candidate set, but to generate the candidate nodes in $G_{large}$ for a given node $u\in V_{small}$.
  53.622 +In case of an expanding problem type and $M$ mapping, if a node $v\in V_{large}$ is a potential pair of $u\in V_{small}$, then $\forall u'\in V_{small} : (u,u')\in E_{small}\ and\ u'\ is\ covered\ by\ M\ \Rightarrow (v,Pair(M,u'))\in E_{large}$. That is, each covered neighbour of $u$ has to be mapped to a covered neighbour of $v$.
  53.623 +
  53.624 +Having said that, an algorithm running in $\Theta(deg)$ time is describable if there exists a covered node in the component containing $u$. In this case choose a covered neighbour $u'$ of $u$ arbitrarily --- such a node exists based on \textbf{Claim~\ref{claim:MOclaim})}. With all the candidates of $u$ being among the uncovered neighbours of $Pair(M,u')$, there are solely $deg(Pair(M,u'))$ nodes to check.
  53.625 +
  53.626 +An easy trick is to choose an $u'$, for which $|\{uncovered\ neighbours\ $ $of\ Pair(M,u')\}|$ is the smallest possible.
  53.627 +
  53.628 +Note that if $u$ is the first node of its component, then all the uncovered nodes of $G_{large}$ are candidates, so giving a sublinear method is impossible.
  53.629 +
  53.630 +
  53.631 +\subsubsection{Determining the node order}
  53.632 +This section describes how the node order preprocessing method of VF2++ can efficiently be implemented.
  53.633 +
  53.634 +For using lookup tables, the node labels are associated with the numbers $\{0,1,..,|K|-1\}$, where $K$ is the set of the labels. It enables $F_\mathcal{M}$ to be stored in an array, for which $F_\mathcal{M}[i]=F_\mathcal{M}(i)$ where $i=0,1,..,|K|-1$. At first, $\mathcal{M}=\emptyset$, so $F_\mathcal{M}[i]$ is the number of nodes in $V_{small}$ having label i, which is easy to compute in $\Theta(|V_{small}|)$ steps.
  53.635 +
  53.636 +$\mathcal{M}\subseteq V_{small}$ can be represented as an array of size $|V_{small}|$.
  53.637 +
  53.638 +The BFS tree is computed by using a FIFO data structure which is usually implemented as a linked list, but one can avoid it by using the array $\mathcal{M}$ itself. $\mathcal{M}$ contains all the nodes seen before, a pointer shows where the first node of the FIFO is, and another one shows where the next explored node has to be inserted. So the nodes of each level of the BFS tree can be processed by \textbf{Algorithm \ref{alg:VF2PPProcess1})} and \textbf{\ref{alg:VF2PPProcess2})} in place by swapping nodes.
  53.639 +
  53.640 +After a node $u$ gets to the next place of the node order, $F_\mathcal{M}[lab[u]]$ has to be decreased by one, because there is one less covered node in $V_{large}$ with label $lab(u)$, that is why min selection sort is preferred which gives the elements from left to right in descending order, see \textbf{Algorithm \ref{alg:VF2PPProcess1})}.
  53.641 +
  53.642 +Note that using a $\Theta(n^2)$ sort absolutely does not slow down the procedure on biological (and on sparse) graphs, since they have few nodes on a level. If a level had a large number of nodes, \textbf{Algorithm \ref{alg:VF2PPProcess2})} would seem to be a better choice with a $\Theta(nlog(n))$ or Bucket sort, but it may reduce the efficiency of the matching procedure, since $F_\mathcal{M}(i)$ can not be immediately refreshed, so it is unable to provide up-to-date label information. 
  53.643 +
  53.644 +Note that the \textit{while loop} of \textbf{Algorithm \ref{alg:VF2PPPseu})} takes one iteration per graph component and the graphs in biology are mostly connected.
  53.645 +\subsubsection{Cutting rules}
  53.646 +In \textbf{Section \ref{VF2PPCuttingRules})}, the cutting rules were described using the sets $T_{small}$, $T_{large}$, $\tilde T_{small}$ and $\tilde T_{large}$, which are dependent on the all-time mapping (i.e. on the all-time state). The aim is to check the labeled cutting rules of VF2++ in $\Theta(deg)$ time.
  53.647 +
  53.648 +Firstly, suppose that these four sets are given in such a way, that checking whether a node is in a certain set takes constant time, e.g. they are given by their 0-1 characteristic vectors. Let $L$ be an initially zero integer lookup table of size $|K|$. After incrementing $L[lab(u')]$ for all $u'\in \Gamma_{small}(u) \cap T_{small}(s)$ and decrementing $L[lab(v')]$ for all $v'\in\Gamma_{large} (v) \cap T_{large}(s)$, the first part of the cutting rules is checkable in $\Theta(deg)$ time by considering the proper signs of $L$. Setting $L$ to zero takes $\Theta(deg)$ time again, which makes it possible to use the same table through the whole algorithm.
  53.649 +The second part of the cutting rules can be verified using the same method with $\tilde T_{small}$ and $\tilde T_{large}$ instead of $T_{small}$ and $T_{large}$. Thus, the overall complexity is $\Theta(deg)$.
  53.650 +
  53.651 +An other integer lookup table storing the number of covered neighbours of each node in $G_{large}$ gives all the information about the sets $T_{large}$ and $\tilde T_{large}$, which is maintainable in $\Theta(deg)$ time when a pair is added or substracted by incrementing or decrementing the proper indices. A further improvement is that the values of $L[lab(u')]$ in case of checking $u$ is dependent only on $u$, i.e. on the size of the mapping, so for each $u\in V_{small}$ an array of pairs (label, number of such labels) can be stored to skip the maintaining operations. Note that these arrays are at most of size $deg$. Skipping this trick, the number of covered neighbours has to be stored for each node of $G_{small}$ as well to get the sets $T_{small}$ and $\tilde T_{small}$.
  53.652 +
  53.653 +Using similar tricks, the consistency function can be evaluated in $\Theta(deg)$ steps, as well.
  53.654 +
  53.655 +\section{The VF2 Plus Algorithm}
  53.656 +The VF2 Plus algorithm is a recently improved version of VF2. It was compared with the state of the art algorithms in \cite{VF2Plus} and has proven itself to be competitive with RI, the best algorithm on biological graphs.
  53.657 +\\
  53.658 +A short summary of VF2 Plus follows, which uses the notation and the conventions of the original paper.
  53.659 +
  53.660 +\subsection{Ordering procedure}
  53.661 +VF2 Plus uses a sorting procedure that prefers nodes in $V_{small}$ with the lowest probability to find a pair in $V_{small}$ and the highest number of connections with the nodes already sorted by the algorithm.
  53.662 +
  53.663 +\begin{definition}
  53.664 +$(u,v)$ is a \textbf{feasible pair}, if $lab(u)=lab(v)$ and $deg(u)\leq deg(v)$, where $u\in{V_{small}}$ and $ v\in{V_{large}}$. 
  53.665 +\end{definition}
  53.666 +$P_{lab}(L):=$ a priori probability to find a node with label $L$ in $V_{large}$
  53.667 +\newline
  53.668 +$P_{deg}(d):=$ a priori probability to find a node with degree $d$ in $V_{large}$
  53.669 +\newline
  53.670 +$P(u):=P_{lab}(L)*\bigcup_{d'>d}P_{deg}(d')$\\
  53.671 +$M$ is the set of already sorted nodes, $T$ is the set of nodes candidate to be selected, and $degreeM$ of a node is the number of its neighbours in $M$.
  53.672 +\begin{algorithm}
  53.673 +\algtext*{EndIf}%ne nyomtasson end if-et
  53.674 +\algtext*{EndFor}%ne nyomtasson ..
  53.675 +\algtext*{EndProcedure}%ne nyomtasson ..
  53.676 +\algtext*{EndWhile}
  53.677 +\caption{}\label{alg:VF2PlusPseu}
  53.678 +\begin{algorithmic}[1]
  53.679 +\Procedure{VF2 Plus order}{}
  53.680 +  \State Select the node with the lowest $P$.
  53.681 +    \If {more nodes share the same $P$}
  53.682 +    \State select the one with maximum degree
  53.683 +    \EndIf
  53.684 +    \If {more nodes share the same $P$ and have the max degree}
  53.685 +    \State select the first
  53.686 +    \EndIf
  53.687 +  \State Put the selected node in the set $M$. \label{alg:putIn}
  53.688 +  \State Put all its unsorted neighbours in the set $T$.
  53.689 +  \If {$M\neq V_{small}$}
  53.690 +  \State From set $T$ select the node with maximum $degreeM$.
  53.691 +  \If {more nodes have maximum $degreeM$}
  53.692 +    \State Select the one with the lowest $P$
  53.693 +  \EndIf
  53.694 +  \If {more nodes have maximum $degreeM$ and $P$}
  53.695 +    \State Select the first.
  53.696 +  \EndIf
  53.697 +  \State \textbf{goto \ref{alg:putIn}.}
  53.698 +  \EndIf
  53.699 +\EndProcedure
  53.700 +\end{algorithmic}
  53.701 +\end{algorithm}
  53.702 +
  53.703 +Using these notations, \textbf{Algorithm~\ref{alg:VF2PlusPseu})} provides the description of the sorting procedure.
  53.704 +
  53.705 +Note that $P(u)$ is not the exact probability of finding a consistent pair for $u$ by choosing a node of $V_{large}$ randomly, since $P_{lab}$ and $P_{deg}$ are not independent, though calculating the real probability would take quadratic time, which may be reduced by using fittingly lookup tables.
  53.706 +
  53.707 +\newpage
  53.708 +\section{Experimental results}
  53.709 +This section compares the performance of VF2++ and VF2 Plus. Both algorithms have run faster with orders of magnitude than VF2, thus its inclusion was not reasonable.
  53.710 +\subsection{Biological graphs}
  53.711 +The tests have been executed on a recent biological dataset created for the International Contest on Pattern Search in Biological Databases\cite{Content}, which has been constructed of Molecule, Protein and Contact Map graphs extracted from the Protein Data Bank\cite{ProteinDataBank}.
  53.712 +
  53.713 +The molecule dataset contains small graphs with less than 100 nodes and an average degree of less than 3. The protein dataset contains graphs having 500-10 000 nodes and an average degree of 4, while the contact map dataset contains graphs with 150-800 nodes and an average degree of 20.
  53.714 +\\
  53.715 +
  53.716 +In the following, the induced subgraph isomorphism and the graph isomorphism will be examined.
  53.717 +
  53.718 +\subsubsection{Induced subgraph isomorphism}
  53.719 +This dataset contains a set of graph pairs, and \textbf{all} the induced subgraph ismorphisms have to be found between them. \textbf{Figure \ref{fig:INDProt}), \ref{fig:INDContact}),} and \textbf{ \ref{fig:INDMolecule})} show the solution time of the problems in the problem set.
  53.720 +
  53.721 +\begin{figure}[H]
  53.722 +\begin{center}
  53.723 +\begin{tikzpicture}
  53.724 +  \begin{axis}[title=Proteins IND,xlabel={target size},ylabel={time (ms)},legend entries={VF2 Plus,VF2++},grid
  53.725 +  =major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label        style={/pgf/number format/1000 sep = \thinspace}]
  53.726 +  %\addplot+[only marks] table {proteinsOrig.txt};
  53.727 +  \addplot[mark=*,mark size=1.2pt,color=blue] table {Orig/Proteins.256.txt};
  53.728 +  \addplot[mark=triangle*,mark size=1.8pt,color=red] table {VF2PPLabel/Proteins.256.txt};
  53.729 +  \end{axis}
  53.730 +  \end{tikzpicture}
  53.731 +\end{center}
  53.732 +\vspace*{-0.8cm}
  53.733 +\caption{Both the algorithms have linear behaviour on protein graphs. VF2++ is more than 10 times faster than VF2 Plus.} \label{fig:INDProt}
  53.734 +\end{figure}
  53.735 +
  53.736 +\begin{figure}[H]
  53.737 +\begin{center}
  53.738 +\begin{tikzpicture}
  53.739 +\begin{axis}[title=Contact Maps IND,xlabel={target size},ylabel={time (ms)},legend entries={VF2 Plus,VF2++},grid
  53.740 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \thinspace}]
  53.741 +%\addplot+[only marks] table {proteinsOrig.txt};
  53.742 +\addplot table {Orig/ContactMaps.128.txt};
  53.743 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {VF2PPLabel/ContactMaps.128.txt};
  53.744 +\end{axis}
  53.745 +\end{tikzpicture}
  53.746 +\end{center}
  53.747 +\vspace*{-0.8cm}
  53.748 +\caption{On Contact Maps, VF2++ runs in near constant time, while VF2 Plus has a near linear behaviour.} \label{fig:INDContact}
  53.749 +\end{figure}
  53.750 +
  53.751 +\begin{figure}[H]
  53.752 +\begin{center}
  53.753 +\begin{tikzpicture}
  53.754 +\begin{axis}[title=Molecules IND,xlabel={target size},ylabel={time (ms)},legend entries={VF2 Plus,VF2++},grid
  53.755 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \thinspace}]
  53.756 +%\addplot+[only marks] table {proteinsOrig.txt};
  53.757 +\addplot table {Orig/Molecules.32.txt};
  53.758 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {VF2PPLabel/Molecules.32.txt};
  53.759 +\end{axis}
  53.760 +\end{tikzpicture}
  53.761 +\end{center}
  53.762 +\vspace*{-0.8cm}
  53.763 +\caption{In the case of Molecules, the algorithms seem to have a similar behaviour, but VF2++ is almost two times faster even on such small graphs.} \label{fig:INDMolecule}
  53.764 +\end{figure}
  53.765 +
  53.766 +
  53.767 +\subsubsection{Graph ismorphism}
  53.768 +In this experiment, the nodes of each graph in the database have been shuffled and an isomorphism between the shuffled and the original graph has been searched. For runtime results, see \textbf{Figure \ref{fig:ISOProt}), \ref{fig:ISOContact}),} and \textbf{\ref{fig:ISOMolecule})}.
  53.769 +\begin{figure}[H]
  53.770 +\begin{center}
  53.771 +\begin{tikzpicture}
  53.772 +\begin{axis}[title=Proteins ISO,xlabel={target size},ylabel={time (ms)},legend entries={VF2 Plus,VF2++},grid
  53.773 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \thinspace}]
  53.774 +%\addplot+[only marks] table {proteinsOrig.txt};
  53.775 +\addplot table {Orig/proteinsIso.txt};
  53.776 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {VF2PPLabel/proteinsIso.txt};
  53.777 +\end{axis}
  53.778 +\end{tikzpicture}
  53.779 +\end{center}
  53.780 +\vspace*{-0.8cm}
  53.781 +\caption{On protein graphs, VF2 Plus has a super linear time complexity, while VF2++ runs in near constant time. The difference is about two order of magnitude on large graphs.}\label{fig:ISOProt}
  53.782 +\end{figure}
  53.783 +
  53.784 +\begin{figure}[H]
  53.785 +\begin{center}
  53.786 +\begin{tikzpicture}
  53.787 +\begin{axis}[title=Contact Maps ISO,xlabel={target size},ylabel={time (ms)},legend entries={VF2 Plus,VF2++},grid
  53.788 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \thinspace}]
  53.789 +%\addplot+[only marks] table {proteinsOrig.txt};
  53.790 +\addplot table {Orig/contactMapsIso.txt};
  53.791 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {VF2PPLabel/contactMapsIso.txt};
  53.792 +\end{axis}
  53.793 +\end{tikzpicture}
  53.794 +\end{center}
  53.795 +\vspace*{-0.8cm}
  53.796 +\caption{The results are closer to each other on Contact Maps, but VF2++ still performs consistently better.}\label{fig:ISOContact}
  53.797 +\end{figure}
  53.798 +
  53.799 +\begin{figure}[H]
  53.800 +\begin{center}
  53.801 +\begin{tikzpicture}
  53.802 +\begin{axis}[title=Molecules ISO,xlabel={target size},ylabel={time (ms)},legend entries={VF2 Plus,VF2++},grid
  53.803 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \thinspace}]
  53.804 +%\addplot+[only marks] table {proteinsOrig.txt};
  53.805 +\addplot table {Orig/moleculesIso.txt};
  53.806 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {VF2PPLabel/moleculesIso.txt};
  53.807 +\end{axis}
  53.808 +\end{tikzpicture}
  53.809 +\end{center}
  53.810 +\vspace*{-0.8cm}
  53.811 +\caption{In the case of Molecules, there is not such a significant difference, but VF2++ seems to be faster as the number of nodes increases.}\label{fig:ISOMolecule}
  53.812 +\end{figure}
  53.813 +
  53.814 +
  53.815 +\subsection{Random graphs}
  53.816 +This section compares VF2++ with VF2 Plus on random graphs of a large size. The node labels are uniformly distributed.
  53.817 +Let $\delta$ denote the average degree.
  53.818 +For the parameters of problems solved in the experiments, please see the top of each chart.
  53.819 +\subsubsection{Graph isomorphism}
  53.820 +To evaluate the efficiency of the algorithms in the case of graph isomorphism, connected graphs of less than 20 000 nodes have been considered. Generating a random graph and shuffling its nodes, an isomorphism had to be found. \textbf{Figure \ref{fig:randISO5}), \ref{fig:randISO10}), \ref{fig:randISO15}), \ref{fig:randISO35}), \ref{fig:randISO45}),} and \textbf{\ref{fig:randISO100}) } show the runtime results on graph sets of various density.
  53.821 +
  53.822 +\begin{figure}[H]
  53.823 +\begin{center}
  53.824 +\begin{tikzpicture}
  53.825 +\begin{axis}[title={Random ISO, $\delta = 5$},xlabel={target size},ylabel={time (ms)},legend entries={VF2 Plus,VF2++},grid
  53.826 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \thinspace}]
  53.827 +%\addplot+[only marks] table {proteinsOrig.txt};
  53.828 +\addplot table {randGraph/iso/vf2pIso5_1.txt};
  53.829 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/iso/vf2ppIso5_1.txt};
  53.830 +\end{axis}
  53.831 +\end{tikzpicture}
  53.832 +\end{center}
  53.833 +\vspace*{-0.8cm}
  53.834 +\caption{}\label{fig:randISO5}
  53.835 +\end{figure}
  53.836 +
  53.837 +\begin{figure}[H]
  53.838 +\begin{center}
  53.839 +\begin{tikzpicture}
  53.840 +\begin{axis}[title={Random ISO, $\delta = 10$},xlabel={target size},ylabel={time (ms)},legend entries={VF2 Plus,VF2++},grid
  53.841 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \thinspace}]
  53.842 +%\addplot+[only marks] table {proteinsOrig.txt};
  53.843 +\addplot table {randGraph/iso/vf2pIso10_1.txt};
  53.844 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/iso/vf2ppIso10_1.txt};
  53.845 +\end{axis}
  53.846 +\end{tikzpicture}
  53.847 +\end{center}
  53.848 +\vspace*{-0.8cm}
  53.849 +\caption{}\label{fig:randISO10}
  53.850 +\end{figure}
  53.851 +
  53.852 +\begin{figure}[H]
  53.853 +\begin{center}
  53.854 +\begin{tikzpicture}
  53.855 +\begin{axis}[title={Random ISO, $\delta = 15$},xlabel={target size},ylabel={time (ms)},legend entries={VF2 Plus,VF2++},grid
  53.856 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \thinspace}]
  53.857 +%\addplot+[only marks] table {proteinsOrig.txt};
  53.858 +\addplot table {randGraph/iso/vf2pIso15_1.txt};
  53.859 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/iso/vf2ppIso15_1.txt};
  53.860 +\end{axis}
  53.861 +\end{tikzpicture}
  53.862 +\end{center}
  53.863 +\vspace*{-0.8cm}
  53.864 +\caption{}\label{fig:randISO15}
  53.865 +\end{figure}
  53.866 +
  53.867 +\begin{figure}[H]
  53.868 +\begin{center}
  53.869 +\begin{tikzpicture}
  53.870 +\begin{axis}[title={Random ISO, $\delta = 35$},xlabel={target size},ylabel={time (ms)},legend entries={VF2 Plus,VF2++},grid
  53.871 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \thinspace}]
  53.872 +%\addplot+[only marks] table {proteinsOrig.txt};
  53.873 +\addplot table {randGraph/iso/vf2pIso35_1.txt};
  53.874 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/iso/vf2ppIso35_1.txt};
  53.875 +\end{axis}
  53.876 +\end{tikzpicture}
  53.877 +\end{center}
  53.878 +\vspace*{-0.8cm}
  53.879 +\caption{}\label{fig:randISO35}
  53.880 +\end{figure}
  53.881 +
  53.882 +\begin{figure}[H]
  53.883 +\begin{center}
  53.884 +\begin{tikzpicture}
  53.885 +\begin{axis}[title={Random ISO, $\delta = 45$},xlabel={target size},ylabel={time (ms)},legend entries={VF2 Plus,VF2++},grid
  53.886 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \thinspace}]
  53.887 +%\addplot+[only marks] table {proteinsOrig.txt};
  53.888 +\addplot table {randGraph/iso/vf2pIso45_1.txt};
  53.889 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/iso/vf2ppIso45_1.txt};
  53.890 +\end{axis}
  53.891 +\end{tikzpicture}
  53.892 +\end{center}
  53.893 +\vspace*{-0.8cm}
  53.894 +\caption{}\label{fig:randISO45}
  53.895 +\end{figure}
  53.896 +
  53.897 +\begin{figure}[H]
  53.898 +\begin{center}
  53.899 +\begin{tikzpicture}
  53.900 +\begin{axis}[title={Random ISO, $\delta = 100$},xlabel={target size},ylabel={time (ms)},legend entries={VF2 Plus,VF2++},grid
  53.901 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \thinspace}]
  53.902 +%\addplot+[only marks] table {proteinsOrig.txt};
  53.903 +\addplot table {randGraph/iso/vf2pIso100_1.txt};
  53.904 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/iso/vf2ppIso100_1.txt};
  53.905 +\end{axis}
  53.906 +\end{tikzpicture}
  53.907 +\end{center}
  53.908 +\vspace*{-0.8cm}
  53.909 +\caption{}\label{fig:randISO100}
  53.910 +\end{figure}
  53.911 +
  53.912 +
  53.913 +Considering the graph isomorphism problem, VF2++ consistently outperforms its rival especially on sparse graphs. The reason for the slightly super linear behaviour of VF2++ on denser graphs is the larger number of nodes in the BFS tree constructed in \textbf{Algorithm \ref{alg:VF2PPPseu})}.
  53.914 +
  53.915 +\subsubsection{Induced subgraph isomorphism}
  53.916 +This section provides a comparison of VF2++ and VF2 Plus in the case of induced subgraph isomorphism. In addition to the size of the large graph, that of the small graph dramatically influences the hardness of a given problem too, so the overall picture is provided by examining small graphs of various size.
  53.917 +
  53.918 +For each chart, a number $0<\rho< 1$ has been fixed and the following has been executed 150 times. Generating a large graph $G_{large}$, choose 10 of its induced subgraphs having $\rho\ |V_{large}|$ nodes, and for all the 10 subgraphs find a mapping by using both the graph matching algorithms.
  53.919 +The $\delta = 5, 10, 35$ and $\rho = 0.05, 0.1, 0.3, 0.6, 0.8, 0.95$ cases have been examined (see \textbf{Figure \ref{fig:randIND5}), \ref{fig:randIND10})} and \textbf{\ref{fig:randIND35})}), and for each $\delta$, a cumulative chart is given as well, which excludes $\rho = 0.05$ and $0.1$ for the sake of perspicuity (see \textbf{Figure \ref{fig:randIND5Sum}), \ref{fig:randIND10Sum})} and \textbf{\ref{fig:randIND35Sum})}).
  53.920 +
  53.921 +
  53.922 +
  53.923 +
  53.924 +
  53.925 +\begin{figure}[H]
  53.926 +\vspace*{-0.8cm}
  53.927 +\begin{subfigure}[b]{0.55\textwidth}
  53.928 +\begin{center}
  53.929 +\begin{tikzpicture}
  53.930 +\begin{axis}[title={Random IND, $\delta = 5$, $\rho = 0.05$},width=7.2cm,height=6cm,xlabel={target size},ylabel={time (ms)},ylabel near ticks,legend entries={VF2 Plus,VF2++},grid
  53.931 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \space}]
  53.932 +%\addplot+[only marks] table {proteinsOrig.txt};
  53.933 +\addplot table {randGraph/ind/vf2pInd5_0.05.txt};
  53.934 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd5_0.05.txt};
  53.935 +\end{axis}
  53.936 +\end{tikzpicture}
  53.937 +\end{center}
  53.938 +     \end{subfigure}
  53.939 +     \begin{subfigure}[b]{0.55\textwidth}
  53.940 +\begin{center}
  53.941 +\begin{tikzpicture}
  53.942 +\begin{axis}[title={Random IND, $\delta = 5$, $\rho = 0.1$},width=7.2cm,height=6cm,xlabel={target size},ylabel={time (ms)},ylabel near ticks,legend entries={VF2 Plus,VF2++},grid
  53.943 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \space}]
  53.944 +%\addplot+[only marks] table {proteinsOrig.txt};
  53.945 +\addplot table {randGraph/ind/vf2pInd5_0.1.txt};
  53.946 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd5_0.1.txt};
  53.947 +\end{axis}
  53.948 +\end{tikzpicture}
  53.949 +\end{center}
  53.950 +\end{subfigure}
  53.951 +\hspace{1cm}
  53.952 +\begin{subfigure}[b]{0.55\textwidth}
  53.953 +\begin{center}
  53.954 +\begin{tikzpicture}
  53.955 +\begin{axis}[title={Random IND, $\delta = 5$, $\rho = 0.3$},width=7.2cm,height=6cm,xlabel={target size},ylabel={time (ms)},ylabel near ticks,legend entries={VF2 Plus,VF2++},grid
  53.956 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \space}]
  53.957 +%\addplot+[only marks] table {proteinsOrig.txt};
  53.958 +\addplot table {randGraph/ind/vf2pInd5_0.3.txt};
  53.959 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd5_0.3.txt};
  53.960 +\end{axis}
  53.961 +\end{tikzpicture}
  53.962 +\end{center}
  53.963 +     \end{subfigure}
  53.964 +     \begin{subfigure}[b]{0.55\textwidth}
  53.965 +\begin{center}
  53.966 +\begin{tikzpicture}
  53.967 +\begin{axis}[title={Random IND, $\delta = 5$, $\rho = 0.6$},width=7.2cm,height=6cm,xlabel={target size},ylabel={time (ms)},ylabel near ticks,legend entries={VF2 Plus,VF2++},grid
  53.968 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \space}]
  53.969 +%\addplot+[only marks] table {proteinsOrig.txt};
  53.970 +\addplot table {randGraph/ind/vf2pInd5_0.6.txt};
  53.971 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd5_0.6.txt};
  53.972 +\end{axis}
  53.973 +\end{tikzpicture}
  53.974 +\end{center}
  53.975 +\end{subfigure}
  53.976 +\begin{subfigure}[b]{0.55\textwidth}
  53.977 +          
  53.978 +\begin{tikzpicture}
  53.979 +\begin{axis}[title={Random IND, $\delta = 5$, $\rho = 0.8$},width=7.2cm,height=6cm,xlabel={target size},ylabel={time (ms)},ylabel near ticks,legend entries={VF2 Plus,VF2++},grid
  53.980 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \space}]
  53.981 +%\addplot+[only marks] table {proteinsOrig.txt};
  53.982 +\addplot table {randGraph/ind/vf2pInd5_0.8.txt};
  53.983 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd5_0.8.txt};
  53.984 +\end{axis}
  53.985 +\end{tikzpicture}
  53.986 +     \end{subfigure}
  53.987 +     \begin{subfigure}[b]{0.55\textwidth}
  53.988 +\begin{tikzpicture}
  53.989 +\begin{axis}[title={Random IND, $\delta = 5$, $\rho = 0.95$},width=7.2cm,height=6cm,xlabel={target size},ylabel={time (ms)},ylabel near ticks,legend entries={VF2 Plus,VF2++},grid
  53.990 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \thinspace}]
  53.991 +%\addplot+[only marks] table {proteinsOrig.txt};
  53.992 +\addplot table {randGraph/ind/vf2pInd5_0.95.txt};
  53.993 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd5_0.95.txt};
  53.994 +\end{axis}
  53.995 +\end{tikzpicture}
  53.996 +\end{subfigure}
  53.997 +\vspace*{-0.8cm}
  53.998 +\caption{IND on graphs having an average degree of 5.}\label{fig:randIND5}
  53.999 +\end{figure}
 53.1000 +
 53.1001 +\begin{figure}[H]
 53.1002 +\begin{center}
 53.1003 +\begin{tikzpicture}
 53.1004 +\begin{axis}[title={Rand IND Summary, $\delta = 5$, $\rho = 0.3, 0.6, 0.8, 0.95$},height=17cm,width=16cm,xlabel={target size},ylabel={time (ms)},legend entries={VF2 Plus,VF2++},line width=0.8pt,grid
 53.1005 +=major,mark size=1pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \thinspace}]
 53.1006 +%\addplot+[only marks] table {proteinsOrig.txt};
 53.1007 +\addplot[mark=*,mark size=1.5pt,color=blue] table {randGraph/ind/vf2pInd5_0.3.txt};
 53.1008 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd5_0.3.txt};
 53.1009 +\addplot[mark=*,mark size=1.5pt,color=blue] table {randGraph/ind/vf2pInd5_0.6.txt};
 53.1010 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd5_0.6.txt};
 53.1011 +\addplot[mark=*,mark size=1.5pt,color=blue] table {randGraph/ind/vf2pInd5_0.8.txt};
 53.1012 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd5_0.8.txt};
 53.1013 +\addplot[mark=*,mark size=1.5pt,color=blue] table {randGraph/ind/vf2pInd5_0.95.txt};
 53.1014 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd5_0.95.txt};
 53.1015 +\end{axis}
 53.1016 +\end{tikzpicture}
 53.1017 +\end{center}
 53.1018 +\vspace*{-0.8cm}
 53.1019 +\caption{Cummulative chart for $\delta=5$.}\label{fig:randIND5Sum}
 53.1020 +\end{figure}
 53.1021 +
 53.1022 +
 53.1023 +
 53.1024 +\begin{figure}[H]
 53.1025 +\vspace*{-0.8cm}
 53.1026 +\begin{subfigure}[b]{0.55\textwidth}
 53.1027 +\begin{center}
 53.1028 +\begin{tikzpicture}
 53.1029 +\begin{axis}[title={Random IND, $\delta = 10$, $\rho = 0.05$},width=7.2cm,height=6cm,xlabel={target size},ylabel={time (ms)},ylabel near ticks,legend entries={VF2 Plus,VF2++},grid
 53.1030 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \space}]
 53.1031 +%\addplot+[only marks] table {proteinsOrig.txt};
 53.1032 +\addplot table {randGraph/ind/vf2pInd10_0.05.txt};
 53.1033 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd10_0.05.txt};
 53.1034 +\end{axis}
 53.1035 +\end{tikzpicture}
 53.1036 +\end{center}
 53.1037 +     \end{subfigure}
 53.1038 +     \begin{subfigure}[b]{0.55\textwidth}
 53.1039 +\begin{center}
 53.1040 +\begin{tikzpicture}
 53.1041 +\begin{axis}[title={Random IND, $\delta = 10$, $\rho = 0.1$},width=7.2cm,height=6cm,xlabel={target size},ylabel={time (ms)},ylabel near ticks,legend entries={VF2 Plus,VF2++},grid
 53.1042 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \space}]
 53.1043 +%\addplot+[only marks] table {proteinsOrig.txt};
 53.1044 +\addplot table {randGraph/ind/vf2pInd10_0.1.txt};
 53.1045 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd10_0.1.txt};
 53.1046 +\end{axis}
 53.1047 +\end{tikzpicture}
 53.1048 +\end{center}
 53.1049 +\end{subfigure}
 53.1050 +\hspace{1cm}
 53.1051 +\begin{subfigure}[b]{0.55\textwidth}
 53.1052 +\begin{center}
 53.1053 +\begin{tikzpicture}
 53.1054 +\begin{axis}[title={Random IND, $\delta = 10$, $\rho = 0.3$},width=7.2cm,height=6cm,xlabel={target size},ylabel={time (ms)},ylabel near ticks,legend entries={VF2 Plus,VF2++},grid
 53.1055 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \space}]
 53.1056 +%\addplot+[only marks] table {proteinsOrig.txt};
 53.1057 +\addplot table {randGraph/ind/vf2pInd10_0.3.txt};
 53.1058 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd10_0.3.txt};
 53.1059 +\end{axis}
 53.1060 +\end{tikzpicture}
 53.1061 +\end{center}
 53.1062 +     \end{subfigure}
 53.1063 +     \begin{subfigure}[b]{0.55\textwidth}
 53.1064 +\begin{center}
 53.1065 +\begin{tikzpicture}
 53.1066 +\begin{axis}[title={Random IND, $\delta = 10$, $\rho = 0.6$},width=7.2cm,height=6cm,xlabel={target size},ylabel={time (ms)},ylabel near ticks,legend entries={VF2 Plus,VF2++},grid
 53.1067 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \space}]
 53.1068 +%\addplot+[only marks] table {proteinsOrig.txt};
 53.1069 +\addplot table {randGraph/ind/vf2pInd10_0.6.txt};
 53.1070 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd10_0.6.txt};
 53.1071 +\end{axis}
 53.1072 +\end{tikzpicture}
 53.1073 +\end{center}
 53.1074 +\end{subfigure}
 53.1075 +\begin{subfigure}[b]{0.55\textwidth}
 53.1076 +          
 53.1077 +\begin{tikzpicture}
 53.1078 +\begin{axis}[title={Random IND, $\delta = 10$, $\rho = 0.8$},width=7.2cm,height=6cm,xlabel={target size},ylabel={time (ms)},ylabel near ticks,legend entries={VF2 Plus,VF2++},grid
 53.1079 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \space}]
 53.1080 +%\addplot+[only marks] table {proteinsOrig.txt};
 53.1081 +\addplot table {randGraph/ind/vf2pInd10_0.8.txt};
 53.1082 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd10_0.8.txt};
 53.1083 +\end{axis}
 53.1084 +\end{tikzpicture}
 53.1085 +     \end{subfigure}
 53.1086 +     \begin{subfigure}[b]{0.55\textwidth}
 53.1087 +\begin{tikzpicture}
 53.1088 +\begin{axis}[title={Random IND, $\delta = 10$, $\rho = 0.95$},width=7.2cm,height=6cm,xlabel={target size},ylabel={time (ms)},ylabel near ticks,legend entries={VF2 Plus,VF2++},grid
 53.1089 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \thinspace}]
 53.1090 +%\addplot+[only marks] table {proteinsOrig.txt};
 53.1091 +\addplot table {randGraph/ind/vf2pInd10_0.95.txt};
 53.1092 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd10_0.95.txt};
 53.1093 +\end{axis}
 53.1094 +\end{tikzpicture}
 53.1095 +\end{subfigure}
 53.1096 +\vspace*{-0.8cm}
 53.1097 +\caption{IND on graphs having an average degree of 10.}\label{fig:randIND10}
 53.1098 +\end{figure}
 53.1099 +
 53.1100 +\begin{figure}[H]
 53.1101 +\begin{center}
 53.1102 +\begin{tikzpicture}
 53.1103 +\begin{axis}[title={Rand IND Summary, $\delta = 10$, $\rho = 0.3, 0.6, 0.8, 0.95$},height=17cm,width=16cm,xlabel={target size},ylabel={time (ms)},legend entries={VF2 Plus,VF2++},line width=0.8pt,grid
 53.1104 +=major,mark size=1pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \thinspace}]
 53.1105 +%\addplot+[only marks] table {proteinsOrig.txt};
 53.1106 +\addplot[mark=*,mark size=1.5pt,color=blue] table {randGraph/ind/vf2pInd10_0.3.txt};
 53.1107 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd10_0.3.txt};
 53.1108 +\addplot[mark=*,mark size=1.5pt,color=blue] table {randGraph/ind/vf2pInd10_0.6.txt};
 53.1109 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd10_0.6.txt};
 53.1110 +\addplot[mark=*,mark size=1.5pt,color=blue] table {randGraph/ind/vf2pInd10_0.8.txt};
 53.1111 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd10_0.8.txt};
 53.1112 +\addplot[mark=*,mark size=1.5pt,color=blue] table {randGraph/ind/vf2pInd10_0.95.txt};
 53.1113 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd10_0.95.txt};
 53.1114 +\end{axis}
 53.1115 +\end{tikzpicture}
 53.1116 +\end{center}
 53.1117 +\vspace*{-0.8cm}
 53.1118 +\caption{Cummulative chart for $\delta=10$.}\label{fig:randIND10Sum}
 53.1119 +\end{figure}
 53.1120 +
 53.1121 +
 53.1122 +
 53.1123 +\begin{figure}[H]
 53.1124 +\vspace*{-0.8cm}
 53.1125 +\begin{subfigure}[b]{0.55\textwidth}
 53.1126 +\begin{center}
 53.1127 +\begin{tikzpicture}
 53.1128 +\begin{axis}[title={Random IND, $\delta = 35$, $\rho = 0.05$},width=7.2cm,height=6cm,xlabel={target size},ylabel={time (ms)},ylabel near ticks,legend entries={VF2 Plus,VF2++},grid
 53.1129 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \space}]
 53.1130 +%\addplot+[only marks] table {proteinsOrig.txt};
 53.1131 +\addplot table {randGraph/ind/vf2pInd35_0.05.txt};
 53.1132 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd35_0.05.txt};
 53.1133 +\end{axis}
 53.1134 +\end{tikzpicture}
 53.1135 +\end{center}
 53.1136 +     \end{subfigure}
 53.1137 +     \begin{subfigure}[b]{0.55\textwidth}
 53.1138 +\begin{center}
 53.1139 +\begin{tikzpicture}
 53.1140 +\begin{axis}[title={Random IND, $\delta = 35$, $\rho = 0.1$},width=7.2cm,height=6cm,xlabel={target size},ylabel={time (ms)},ylabel near ticks,legend entries={VF2 Plus,VF2++},grid
 53.1141 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \space}]
 53.1142 +%\addplot+[only marks] table {proteinsOrig.txt};
 53.1143 +\addplot table {randGraph/ind/vf2pInd35_0.1.txt};
 53.1144 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd35_0.1.txt};
 53.1145 +\end{axis}
 53.1146 +\end{tikzpicture}
 53.1147 +\end{center}
 53.1148 +\end{subfigure}
 53.1149 +\hspace{1cm}
 53.1150 +\begin{subfigure}[b]{0.55\textwidth}
 53.1151 +\begin{center}
 53.1152 +\begin{tikzpicture}
 53.1153 +\begin{axis}[title={Random IND, $\delta = 35$, $\rho = 0.3$},width=7.2cm,height=6cm,xlabel={target size},ylabel={time (ms)},ylabel near ticks,legend entries={VF2 Plus,VF2++},grid
 53.1154 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \space}]
 53.1155 +%\addplot+[only marks] table {proteinsOrig.txt};
 53.1156 +\addplot table {randGraph/ind/vf2pInd35_0.3.txt};
 53.1157 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd35_0.3.txt};
 53.1158 +\end{axis}
 53.1159 +\end{tikzpicture}
 53.1160 +\end{center}
 53.1161 +     \end{subfigure}
 53.1162 +     \begin{subfigure}[b]{0.55\textwidth}
 53.1163 +\begin{center}
 53.1164 +\begin{tikzpicture}
 53.1165 +\begin{axis}[title={Random IND, $\delta = 35$, $\rho = 0.6$},width=7.2cm,height=6cm,xlabel={target size},ylabel={time (ms)},ylabel near ticks,legend entries={VF2 Plus,VF2++},grid
 53.1166 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \space}]
 53.1167 +%\addplot+[only marks] table {proteinsOrig.txt};
 53.1168 +\addplot table {randGraph/ind/vf2pInd35_0.6.txt};
 53.1169 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd35_0.6.txt};
 53.1170 +\end{axis}
 53.1171 +\end{tikzpicture}
 53.1172 +\end{center}
 53.1173 +\end{subfigure}
 53.1174 +\begin{subfigure}[b]{0.55\textwidth}
 53.1175 +          
 53.1176 +\begin{tikzpicture}
 53.1177 +\begin{axis}[title={Random IND, $\delta = 35$, $\rho = 0.8$},width=7.2cm,height=6cm,xlabel={target size},ylabel={time (ms)},ylabel near ticks,legend entries={VF2 Plus,VF2++},grid
 53.1178 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \space}]
 53.1179 +%\addplot+[only marks] table {proteinsOrig.txt};
 53.1180 +\addplot table {randGraph/ind/vf2pInd35_0.8.txt};
 53.1181 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd35_0.8.txt};
 53.1182 +\end{axis}
 53.1183 +\end{tikzpicture}
 53.1184 +     \end{subfigure}
 53.1185 +     \begin{subfigure}[b]{0.55\textwidth}
 53.1186 +\begin{tikzpicture}
 53.1187 +\begin{axis}[title={Random IND, $\delta = 35$, $\rho = 0.95$},width=7.2cm,height=6cm,xlabel={target size},ylabel={time (ms)},ylabel near ticks,legend entries={VF2 Plus,VF2++},grid
 53.1188 +=major,mark size=1.2pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \thinspace}]
 53.1189 +%\addplot+[only marks] table {proteinsOrig.txt};
 53.1190 +\addplot table {randGraph/ind/vf2pInd35_0.95.txt};
 53.1191 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd35_0.95.txt};
 53.1192 +\end{axis}
 53.1193 +\end{tikzpicture}
 53.1194 +\end{subfigure}
 53.1195 +\vspace*{-0.8cm}
 53.1196 +\caption{IND on graphs having an average degree of 35.}\label{fig:randIND35}
 53.1197 +\end{figure}
 53.1198 +
 53.1199 +\begin{figure}[H]
 53.1200 +\begin{center}
 53.1201 +\begin{tikzpicture}
 53.1202 +\begin{axis}[title={Rand IND Summary, $\delta = 35$, $\rho = 0.3, 0.6, 0.8, 0.95$},height=17cm,width=16cm,xlabel={target size},ylabel={time (ms)},legend entries={VF2 Plus,VF2++},line width=0.8pt,grid
 53.1203 +=major,mark size=1pt, legend style={at={(0,1)},anchor=north west},scaled x ticks = false,x tick label style={/pgf/number format/1000 sep = \thinspace}]
 53.1204 +%\addplot+[only marks] table {proteinsOrig.txt};
 53.1205 +\addplot[mark=*,mark size=1.5pt,color=blue] table {randGraph/ind/vf2pInd35_0.3.txt};
 53.1206 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd35_0.3.txt};
 53.1207 +\addplot[mark=*,mark size=1.5pt,color=blue] table {randGraph/ind/vf2pInd35_0.6.txt};
 53.1208 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd35_0.6.txt};
 53.1209 +\addplot[mark=*,mark size=1.5pt,color=blue] table {randGraph/ind/vf2pInd35_0.8.txt};
 53.1210 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd35_0.8.txt};
 53.1211 +\addplot[mark=*,mark size=1.5pt,color=blue] table {randGraph/ind/vf2pInd35_0.95.txt};
 53.1212 +\addplot[mark=triangle*,mark size=1.8pt,color=red] table {randGraph/ind/vf2ppInd35_0.95.txt};
 53.1213 +\end{axis}
 53.1214 +\end{tikzpicture}
 53.1215 +\end{center}
 53.1216 +\vspace*{-0.8cm}
 53.1217 +\caption{Cummulative chart for $\delta=35$.}\label{fig:randIND35Sum}
 53.1218 +\end{figure}
 53.1219 +
 53.1220 +Based on these experiments, VF2++ is faster than VF2 Plus and able to handle really large graphs in milliseconds. Note that when $IND$ was considered and the small graphs had proportionally few nodes ($\rho = 0.05$, or $\rho = 0.1$), then VF2 Plus produced some inefficient node orders(e.g. see the $\delta=10$ case on \textbf{Figure \ref{fig:randIND10})}). If these examples had been excluded, the charts would have seemed to be similar to the other ones.
 53.1221 +Unsurprisingly, as denser graphs are considered, both VF2++ and VF2 Plus slow slightly down, but remain practically usable even on graphs having 10 000 nodes.
 53.1222 +
 53.1223 +
 53.1224 +
 53.1225 +
 53.1226 +\newpage
 53.1227 +\section{Conclusion}
 53.1228 +In this thesis, after providing a short summary of the recent algorithms, a new graph matching algorithm based on VF2, called VF2++, has been presented and analyzed from a practical viewpoint.
 53.1229 +
 53.1230 +Recognizing the importance of the node order and determining an efficient one, VF2++ is able to match graphs of thousands of nodes in near practically linear time including preprocessing. In addition to the proper order, VF2++ uses more efficient consistency and cutting rules which are easy to compute and make the algorithm able to prune most of the unfruitful branches without going astray.
 53.1231 +
 53.1232 +In order to show the efficiency of the new method, it has been compared to VF2 Plus, which is the best concurrent algorithm based on \cite{VF2Plus}.
 53.1233 +
 53.1234 +The experiments show that VF2++ consistently outperforms VF2 Plus on biological graphs. It seems to be asymptotically faster on protein and on contact map graphs in the case of induced subgraph isomorphism, while in the case of graph isomorphism, it has definitely better asymptotic behaviour on protein graphs.
 53.1235 +
 53.1236 +Regarding random sparse graphs, not only has VF2++ proved itself to be faster than VF2 Plus, but it has a practically linear behaviour both in the case of induced subgraph- and graph isomorphism, as well.
 53.1237 +
 53.1238 +
 53.1239  
 53.1240  %% The Appendices part is started with the command \appendix;
 53.1241  %% appendix sections are then done as normal sections
 53.1242 @@ -160,20 +1381,21 @@
 53.1243  %% If you have bibdatabase file and want bibtex to generate the
 53.1244  %% bibitems, please use
 53.1245  %%
 53.1246 -%%  \bibliographystyle{elsarticle-num} 
 53.1247 -%%  \bibliography{<your bibdatabase>}
 53.1248 +\bibliographystyle{elsarticle-num} 
 53.1249 +\bibliography{bibliography}
 53.1250  
 53.1251  %% else use the following coding to input the bibitems directly in the
 53.1252  %% TeX file.
 53.1253  
 53.1254 -\begin{thebibliography}{00}
 53.1255 +%% \begin{thebibliography}{00}
 53.1256  
 53.1257 -%% \bibitem{label}
 53.1258 -%% Text of bibliographic item
 53.1259 +%% %% \bibitem{label}
 53.1260 +%% %% Text of bibliographic item
 53.1261  
 53.1262 -\bibitem{}
 53.1263 +%% \bibitem{}
 53.1264  
 53.1265 -\end{thebibliography}
 53.1266 +%% \end{thebibliography}
 53.1267 +
 53.1268  \end{document}
 53.1269  \endinput
 53.1270  %%
    54.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    54.2 +++ b/proteins.txt	Tue Nov 22 08:15:16 2016 +0100
    54.3 @@ -0,0 +1,6 @@
    54.4 +1	10
    54.5 +2	11
    54.6 +3	15
    54.7 +4	7
    54.8 +1	7
    54.9 +1000	6
    55.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    55.2 +++ b/proteinsBfs.txt	Tue Nov 22 08:15:16 2016 +0100
    55.3 @@ -0,0 +1,234 @@
    55.4 +535	0.0013412
    55.5 +554	0.0007026
    55.6 +571	0.0015756
    55.7 +614	0.0021506
    55.8 +634	0.0007692
    55.9 +636	0.0009666
   55.10 +639	0.0007728
   55.11 +730	0.0007754
   55.12 +731	0.0010338
   55.13 +734	0.000867
   55.14 +735	0.0007172
   55.15 +737	0.0017526
   55.16 +755	0.0007422
   55.17 +760	0.0007674
   55.18 +788	0.0050546
   55.19 +794	0.003566
   55.20 +795	0.000748
   55.21 +802	0.0007864
   55.22 +816	0.001123
   55.23 +819	0.0008854
   55.24 +831	0.0007446
   55.25 +833	0.0008486
   55.26 +838	0.0011482
   55.27 +858	0.0007336
   55.28 +861	0.0009128
   55.29 +874	0.000735
   55.30 +877	0.0007424
   55.31 +879	0.0011854
   55.32 +886	0.0009686
   55.33 +899	0.0012188
   55.34 +957	0.000763
   55.35 +982	0.0008034
   55.36 +995	0.0008768
   55.37 +1019	0.00074
   55.38 +1022	0.0007488
   55.39 +1046	0.0028814
   55.40 +1049	0.0008384
   55.41 +1060	0.002723
   55.42 +1073	0.0010472
   55.43 +1076	0.001219
   55.44 +1097	0.0012468
   55.45 +1140	0.0118718
   55.46 +1156	0.000882
   55.47 +1183	0.000859
   55.48 +1192	0.0008868
   55.49 +1202	0.0017446
   55.50 +1227	0.0013412
   55.51 +1271	0.0008776
   55.52 +1300	0.0027128
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    56.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    56.2 +++ b/proteinsOrig.txt	Tue Nov 22 08:15:16 2016 +0100
    56.3 @@ -0,0 +1,234 @@
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    57.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    57.2 +++ b/proteinsOrigDeg.txt	Tue Nov 22 08:15:16 2016 +0100
    57.3 @@ -0,0 +1,234 @@
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  57.139 +2977	0.001369
  57.140 +2991	0.002715
  57.141 +3104	0.003996
  57.142 +3130	0.001376
  57.143 +3131	0.0013916
  57.144 +3134	0.001493
  57.145 +3135	0.001316
  57.146 +3172	0.0039328
  57.147 +3182	0.0013132
  57.148 +3209	0.0014972
  57.149 +3243	0.0014092
  57.150 +3255	0.0015312
  57.151 +3310	0.001293
  57.152 +3366	0.0030994
  57.153 +3429	0.0014398
  57.154 +3459	0.001401
  57.155 +3469	0.0013752
  57.156 +3483	0.004194
  57.157 +3497	0.0025226
  57.158 +3502	0.0131562
  57.159 +3505	0.002496
  57.160 +3515	0.0126334
  57.161 +3517	0.0014942
  57.162 +3522	0.0013314
  57.163 +3523	0.004658
  57.164 +3526	0.0024938
  57.165 +3529	0.0126058
  57.166 +3560	0.0013906
  57.167 +3563	0.0134794
  57.168 +3566	0.0025092
  57.169 +3574	0.0263084
  57.170 +3582	0.0045632
  57.171 +3584	0.012553
  57.172 +3618	0.0016114
  57.173 +3619	0.0123718
  57.174 +3623	0.0014718
  57.175 +3703	0.0013912
  57.176 +3711	0.0016972
  57.177 +3819	0.0017502
  57.178 +3829	0.00524
  57.179 +3839	0.0015298
  57.180 +3870	0.0015676
  57.181 +3906	0.0016762
  57.182 +4025	0.0015506
  57.183 +4083	0.0016758
  57.184 +4156	0.0015202
  57.185 +4194	0.0029256
  57.186 +4220	0.003236
  57.187 +4244	0.0030986
  57.188 +4283	0.0031022
  57.189 +4353	0.0014836
  57.190 +4382	0.0018674
  57.191 +4389	0.0099052
  57.192 +4421	0.0017128
  57.193 +4446	0.0034512
  57.194 +4521	0.0097236
  57.195 +4531	0.0018738
  57.196 +4532	0.005409
  57.197 +4568	0.0016876
  57.198 +4573	0.0019348
  57.199 +4582	0.001692
  57.200 +4604	0.0016946
  57.201 +4629	0.0102874
  57.202 +4710	0.0019622
  57.203 +4713	0.003854
  57.204 +4797	0.001676
  57.205 +4879	0.001759
  57.206 +4970	0.0016564
  57.207 +5059	0.0037634
  57.208 +5126	0.0018568
  57.209 +5241	0.0017572
  57.210 +5254	0.0021308
  57.211 +5271	0.0019392
  57.212 +5318	0.0021702
  57.213 +5346	0.0032566
  57.214 +5455	0.001849
  57.215 +5492	0.0022386
  57.216 +5608	0.0018622
  57.217 +5735	0.0020006
  57.218 +5775	0.0021048
  57.219 +5777	0.0020482
  57.220 +5795	0.002087
  57.221 +5845	0.0039604
  57.222 +5859	0.0069516
  57.223 +5877	0.0066376
  57.224 +5945	0.0020464
  57.225 +5974	0.0122282
  57.226 +5976	0.0020472
  57.227 +5983	0.0020632
  57.228 +6261	0.0046078
  57.229 +6606	0.0025934
  57.230 +6713	0.0019518
  57.231 +6778	0.001855
  57.232 +6883	0.0022792
  57.233 +7349	0.0051702
  57.234 +7453	0.0023572
  57.235 +9114	0.0028286
  57.236 +9174	0.002844
  57.237 +10081	0.0029776
    58.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    58.2 +++ b/randGraph/ind/vf2pInd10_0.05.txt	Tue Nov 22 08:15:16 2016 +0100
    58.3 @@ -0,0 +1,50 @@
    58.4 +354	0.0506667
    58.5 +446	0.0713333
    58.6 +631	0.122
    58.7 +668	0.128667
    58.8 +842	0.192667
    58.9 +1296	0.379333
   58.10 +1327	0.402333
   58.11 +1495	0.486667
   58.12 +1713	0.614333
   58.13 +2027	0.811667
   58.14 +2106	0.911667
   58.15 +2901	1.551
   58.16 +2967	1.64133
   58.17 +3169	1.91167
   58.18 +3279	2.42867
   58.19 +3320	1.978
   58.20 +3510	2.36667
   58.21 +4337	3.20533
   58.22 +4535	3.66033
   58.23 +4841	4.295
   58.24 +5020	4.30967
   58.25 +5111	4.54233
   58.26 +5163	4.843
   58.27 +5359	5.03067
   58.28 +5542	5.158
   58.29 +5547	5.323
   58.30 +5562	5.51767
   58.31 +5631	7.10833
   58.32 +5877	5.91167
   58.33 +6101	10.3863
   58.34 +6295	6.685
   58.35 +6584	7.42
   58.36 +6594	13.237
   58.37 +6788	22.985
   58.38 +6849	10.606
   58.39 +7173	26.576
   58.40 +7279	10.1943
   58.41 +7361	8.77533
   58.42 +7384	11.583
   58.43 +7461	10.739
   58.44 +7467	16.974
   58.45 +8091	11.3097
   58.46 +8451	11.6927
   58.47 +8827	481.983
   58.48 +9031	14.1033
   58.49 +9134	262.166
   58.50 +9427	793.866
   58.51 +9639	14.7117
   58.52 +9720	37.7563
   58.53 +9943	45.4893
    59.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    59.2 +++ b/randGraph/ind/vf2pInd10_0.1.txt	Tue Nov 22 08:15:16 2016 +0100
    59.3 @@ -0,0 +1,48 @@
    59.4 +70	0.0116667
    59.5 +377	0.0986667
    59.6 +390	0.108
    59.7 +788	0.311
    59.8 +1086	0.513333
    59.9 +1922	1.40767
   59.10 +2057	1.694
   59.11 +2071	1.62867
   59.12 +2169	1.81033
   59.13 +2406	2.13267
   59.14 +2958	3.30467
   59.15 +3323	5.543
   59.16 +3631	4.47733
   59.17 +4224	6.646
   59.18 +4380	7.38133
   59.19 +4427	6.581
   59.20 +4663	7.362
   59.21 +4942	10.6473
   59.22 +5118	8.73467
   59.23 +5183	8.83933
   59.24 +5204	11.3987
   59.25 +5368	13.5937
   59.26 +5704	11.7243
   59.27 +5826	14.3633
   59.28 +5859	11.0753
   59.29 +5925	11.8847
   59.30 +5948	12.146
   59.31 +5961	13.188
   59.32 +6052	12.8867
   59.33 +6472	13.8913
   59.34 +6871	17.5173
   59.35 +7015	17.576
   59.36 +7039	261.191
   59.37 +7221	18.2443
   59.38 +7238	17.9493
   59.39 +7776	22.4403
   59.40 +7806	23.5107
   59.41 +8478	23.7227
   59.42 +8679	26.0337
   59.43 +8966	32.3923
   59.44 +9251	46.147
   59.45 +9336	364.076
   59.46 +9499	47.7787
   59.47 +9583	31.54
   59.48 +9585	33.146
   59.49 +9649	312.417
   59.50 +9816	2676
   59.51 +9932	86.0923
    60.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    60.2 +++ b/randGraph/ind/vf2pInd10_0.3.txt	Tue Nov 22 08:15:16 2016 +0100
    60.3 @@ -0,0 +1,50 @@
    60.4 +326	0.229
    60.5 +399	0.312
    60.6 +476	0.405667
    60.7 +1069	1.47167
    60.8 +1389	2.27967
    60.9 +1415	2.38233
   60.10 +1654	3.13433
   60.11 +1909	4.10367
   60.12 +1961	4.20967
   60.13 +2638	7.205
   60.14 +3005	9.56467
   60.15 +3045	9.63067
   60.16 +3144	9.97967
   60.17 +3229	10.535
   60.18 +3275	11.0397
   60.19 +3803	14.7707
   60.20 +4459	19.1907
   60.21 +4816	22.2127
   60.22 +4988	24.2533
   60.23 +5097	24.7153
   60.24 +5424	27.775
   60.25 +5465	28.1747
   60.26 +5634	29.9557
   60.27 +5645	30.4397
   60.28 +6022	34.0627
   60.29 +6094	34.7597
   60.30 +6159	35.3867
   60.31 +6291	36.908
   60.32 +6361	37.735
   60.33 +6638	40.9127
   60.34 +6677	41.3867
   60.35 +6838	43.3643
   60.36 +7043	45.8147
   60.37 +7531	53.295
   60.38 +7566	53.4237
   60.39 +7623	53.3137
   60.40 +7647	53.7857
   60.41 +7822	56.64
   60.42 +7994	58.8747
   60.43 +8003	58.516
   60.44 +8475	65.5097
   60.45 +8996	73.5733
   60.46 +9118	75.6233
   60.47 +9256	78.6417
   60.48 +9702	88.3083
   60.49 +9750	86.066
   60.50 +9753	87.0243
   60.51 +9787	86.666
   60.52 +9848	87.6113
   60.53 +9849	87.6647
    61.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    61.2 +++ b/randGraph/ind/vf2pInd10_0.6.txt	Tue Nov 22 08:15:16 2016 +0100
    61.3 @@ -0,0 +1,50 @@
    61.4 +379	0.659
    61.5 +431	0.756333
    61.6 +665	1.45333
    61.7 +718	1.63233
    61.8 +826	2.04067
    61.9 +1251	4.01467
   61.10 +1279	4.19167
   61.11 +1443	5.15233
   61.12 +1500	5.49767
   61.13 +2193	10.6097
   61.14 +2231	10.9357
   61.15 +2280	11.4147
   61.16 +2632	14.7793
   61.17 +2687	15.294
   61.18 +2907	18.394
   61.19 +3053	19.4757
   61.20 +3091	19.9403
   61.21 +3437	24.123
   61.22 +3587	26.1283
   61.23 +3976	31.5933
   61.24 +4702	43.1907
   61.25 +4751	43.979
   61.26 +5349	54.99
   61.27 +5350	55.042
   61.28 +5353	55.103
   61.29 +5722	64.9803
   61.30 +5764	63.4153
   61.31 +5844	64.99
   61.32 +5946	67.22
   61.33 +5969	68.138
   61.34 +5993	68.2493
   61.35 +6013	68.6733
   61.36 +6323	76.4853
   61.37 +6883	88.9913
   61.38 +6917	89.7673
   61.39 +7218	97.8563
   61.40 +7383	101.738
   61.41 +7663	108.983
   61.42 +8038	120.23
   61.43 +8119	122.024
   61.44 +8133	122.049
   61.45 +8165	123.306
   61.46 +8204	124.93
   61.47 +8694	138.633
   61.48 +8805	142.476
   61.49 +9262	157.005
   61.50 +9334	159.177
   61.51 +9569	167.333
   61.52 +9811	176.083
   61.53 +9876	178.658
    62.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    62.2 +++ b/randGraph/ind/vf2pInd10_0.8.txt	Tue Nov 22 08:15:16 2016 +0100
    62.3 @@ -0,0 +1,50 @@
    62.4 +22	0.031
    62.5 +155	0.288
    62.6 +176	0.334333
    62.7 +911	3.326
    62.8 +1065	4.422
    62.9 +1107	4.559
   62.10 +1526	7.77567
   62.11 +1623	8.72367
   62.12 +1782	10.411
   62.13 +1863	10.9807
   62.14 +1911	11.4317
   62.15 +2165	14.2203
   62.16 +2192	14.5207
   62.17 +2217	14.8703
   62.18 +2247	15.8033
   62.19 +3050	26.4777
   62.20 +3167	28.3113
   62.21 +3398	32.1737
   62.22 +3627	36.211
   62.23 +4092	45.6143
   62.24 +4240	50.091
   62.25 +4346	50.883
   62.26 +4615	56.5223
   62.27 +4673	58.2247
   62.28 +4708	58.7723
   62.29 +4739	59.827
   62.30 +4818	61.338
   62.31 +5058	67.4893
   62.32 +5222	73.828
   62.33 +5414	76.2007
   62.34 +5868	92.0477
   62.35 +5946	90.9583
   62.36 +6061	97.862
   62.37 +6263	101.006
   62.38 +6611	111.016
   62.39 +6699	114.082
   62.40 +6799	118.224
   62.41 +6915	121.078
   62.42 +7100	127.908
   62.43 +7136	128.96
   62.44 +7218	131.624
   62.45 +7369	136.738
   62.46 +7736	150.767
   62.47 +8219	170.233
   62.48 +8377	174.837
   62.49 +8482	178.895
   62.50 +8632	184.569
   62.51 +8886	195.908
   62.52 +9351	215.669
   62.53 +9771	234.352
    63.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    63.2 +++ b/randGraph/ind/vf2pInd10_0.95.txt	Tue Nov 22 08:15:16 2016 +0100
    63.3 @@ -0,0 +1,39 @@
    63.4 +550	1.89167
    63.5 +628	2.30633
    63.6 +660	2.44667
    63.7 +1192	6.26733
    63.8 +1663	11.008
    63.9 +1749	12.0033
   63.10 +2082	16.0437
   63.11 +2355	20.0497
   63.12 +2375	20.4247
   63.13 +2946	31.0957
   63.14 +3499	40.91
   63.15 +3567	42.3037
   63.16 +3774	47.1067
   63.17 +4189	57.4717
   63.18 +4205	57.1887
   63.19 +4214	57.5237
   63.20 +4414	62.6257
   63.21 +4430	65.425
   63.22 +4481	66.262
   63.23 +4500	64.8567
   63.24 +4861	75.0313
   63.25 +5162	83.857
   63.26 +5650	99.221
   63.27 +5724	104.668
   63.28 +5795	107.559
   63.29 +5944	109.123
   63.30 +6006	114.083
   63.31 +6057	113.29
   63.32 +6462	127.495
   63.33 +6536	130.378
   63.34 +6668	135.983
   63.35 +6996	149.48
   63.36 +7594	173.137
   63.37 +7936	188.337
   63.38 +8716	229
   63.39 +9142	250.944
   63.40 +9164	248.217
   63.41 +9435	263.048
   63.42 +9465	264.229
    64.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    64.2 +++ b/randGraph/ind/vf2pInd15_0.05.txt	Tue Nov 22 08:15:16 2016 +0100
    64.3 @@ -0,0 +1,29 @@
    64.4 +216	0.03
    64.5 +407	0.0723333
    64.6 +538	0.105667
    64.7 +927	0.258
    64.8 +1009	0.279667
    64.9 +1277	0.448333
   64.10 +1668	0.648
   64.11 +2391	1.245
   64.12 +3229	2.398
   64.13 +3754	3.21067
   64.14 +3953	2.97767
   64.15 +4254	3.59933
   64.16 +4525	3.90133
   64.17 +4780	4.31133
   64.18 +5281	5.78067
   64.19 +5861	7.20833
   64.20 +6317	7.559
   64.21 +6434	7.90267
   64.22 +6766	7.867
   64.23 +6881	8.46033
   64.24 +7047	8.52233
   64.25 +7316	11.2903
   64.26 +7396	10.8353
   64.27 +8696	25.6483
   64.28 +9051	186.357
   64.29 +9075	51.8077
   64.30 +9377	41.2747
   64.31 +9573	19.3877
   64.32 +9687	27.1643
    65.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    65.2 +++ b/randGraph/ind/vf2pInd15_0.1.txt	Tue Nov 22 08:15:16 2016 +0100
    65.3 @@ -0,0 +1,30 @@
    65.4 +344	0.105333
    65.5 +1434	1.012
    65.6 +2070	1.78833
    65.7 +2175	2.12467
    65.8 +2480	2.36267
    65.9 +2685	2.756
   65.10 +3150	3.74
   65.11 +3611	4.70533
   65.12 +3814	5.17033
   65.13 +4085	6.02267
   65.14 +4089	5.83567
   65.15 +4565	7.13067
   65.16 +4742	7.711
   65.17 +4778	8.84367
   65.18 +5395	11.3127
   65.19 +5587	17.3593
   65.20 +5598	11.304
   65.21 +5741	11.2983
   65.22 +6033	12.098
   65.23 +6357	15.332
   65.24 +6401	14.5977
   65.25 +6581	17.253
   65.26 +6593	14.869
   65.27 +6869	16.6577
   65.28 +7079	19.5183
   65.29 +7280	17.8077
   65.30 +7882	24.0283
   65.31 +8847	26.2117
   65.32 +9039	30.609
   65.33 +9728	33.457
    66.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    66.2 +++ b/randGraph/ind/vf2pInd15_0.2.txt	Tue Nov 22 08:15:16 2016 +0100
    66.3 @@ -0,0 +1,30 @@
    66.4 +32	0.0143333
    66.5 +471	0.318333
    66.6 +1247	1.378
    66.7 +2258	3.965
    66.8 +2333	4.39633
    66.9 +2339	4.09667
   66.10 +2344	4.3
   66.11 +2642	5.072
   66.12 +2756	5.529
   66.13 +3207	7.45267
   66.14 +3593	8.88933
   66.15 +4212	12.124
   66.16 +5038	16.622
   66.17 +5085	16.935
   66.18 +5543	19.945
   66.19 +5801	23.4663
   66.20 +5861	23.88
   66.21 +6042	23.8307
   66.22 +6385	26.9897
   66.23 +6959	31.8693
   66.24 +7205	32.7863
   66.25 +8042	40.4443
   66.26 +8173	41.864
   66.27 +9063	51.899
   66.28 +9074	52.9547
   66.29 +9736	58.821
   66.30 +9770	59.7663
   66.31 +9805	59.3963
   66.32 +9833	64.1883
   66.33 +9914	63.187
    67.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    67.2 +++ b/randGraph/ind/vf2pInd15_0.3.txt	Tue Nov 22 08:15:16 2016 +0100
    67.3 @@ -0,0 +1,30 @@
    67.4 +262	0.207667
    67.5 +598	0.655
    67.6 +694	0.811333
    67.7 +722	0.862
    67.8 +752	0.915667
    67.9 +1116	1.74333
   67.10 +1224	2.021
   67.11 +1293	2.24967
   67.12 +1314	2.264
   67.13 +1836	4.03533
   67.14 +3127	10.3897
   67.15 +3213	10.9287
   67.16 +3390	12.0497
   67.17 +3613	13.491
   67.18 +4832	23.1793
   67.19 +5319	27.7917
   67.20 +5330	28.0533
   67.21 +5379	28.2763
   67.22 +5394	28.4367
   67.23 +5456	29.08
   67.24 +6354	38.7267
   67.25 +6579	41.3643
   67.26 +6889	45.599
   67.27 +7096	47.646
   67.28 +8039	60.601
   67.29 +8436	66.923
   67.30 +8686	71.225
   67.31 +9377	81.8663
   67.32 +9455	82.5453
   67.33 +9608	85.13
    68.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    68.2 +++ b/randGraph/ind/vf2pInd15_0.4.txt	Tue Nov 22 08:15:16 2016 +0100
    68.3 @@ -0,0 +1,30 @@
    68.4 +30	0.023
    68.5 +315	0.366667
    68.6 +439	0.567667
    68.7 +717	1.18
    68.8 +1550	4.17967
    68.9 +1859	5.77533
   68.10 +1867	5.795
   68.11 +1868	5.83467
   68.12 +2687	11.057
   68.13 +2734	11.48
   68.14 +3357	15.9177
   68.15 +3709	19.078
   68.16 +5091	34.3267
   68.17 +5510	39.729
   68.18 +5514	40.0913
   68.19 +5654	42.2553
   68.20 +5732	44.3647
   68.21 +6082	49.7163
   68.22 +6549	57.0103
   68.23 +6816	61.572
   68.24 +6920	62.6347
   68.25 +7859	78.1077
   68.26 +8363	87.6337
   68.27 +8757	97.692
   68.28 +8854	97.8513
   68.29 +8868	98.074
   68.30 +9036	105.005
   68.31 +9515	115.057
   68.32 +9686	118.096
   68.33 +9782	119.309
    69.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    69.2 +++ b/randGraph/ind/vf2pInd15_0.5.txt	Tue Nov 22 08:15:16 2016 +0100
    69.3 @@ -0,0 +1,30 @@
    69.4 +313	0.5
    69.5 +542	1.03933
    69.6 +623	1.258
    69.7 +1531	5.05733
    69.8 +1753	6.40633
    69.9 +1856	7.12267
   69.10 +1903	7.40533
   69.11 +2022	8.23633
   69.12 +2064	8.50633
   69.13 +3364	20.2557
   69.14 +3982	27.4747
   69.15 +4041	29.015
   69.16 +5037	42.9267
   69.17 +6089	60.5607
   69.18 +6443	67.2083
   69.19 +6638	70.898
   69.20 +6892	76.147
   69.21 +7005	79.9043
   69.22 +7133	81.553
   69.23 +7764	97.4677
   69.24 +7826	96.7693
   69.25 +7839	99.9547
   69.26 +7916	99.192
   69.27 +8055	104.416
   69.28 +8075	103.3
   69.29 +8403	111.229
   69.30 +8627	119.201
   69.31 +8701	118.668
   69.32 +9207	134.604
   69.33 +9907	152.308
    70.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    70.2 +++ b/randGraph/ind/vf2pInd15_0.6.txt	Tue Nov 22 08:15:16 2016 +0100
    70.3 @@ -0,0 +1,30 @@
    70.4 +136	0.212333
    70.5 +1037	3.34567
    70.6 +1104	3.686
    70.7 +1198	4.20867
    70.8 +1204	4.26333
    70.9 +1400	5.47233
   70.10 +1533	6.26367
   70.11 +1669	7.33233
   70.12 +1723	7.70567
   70.13 +2230	11.9047
   70.14 +3701	29.3703
   70.15 +4063	35.149
   70.16 +4258	37.7457
   70.17 +4476	41.4307
   70.18 +5205	54.5803
   70.19 +5304	57.3897
   70.20 +5718	65.1257
   70.21 +6123	73.9937
   70.22 +6141	74.5327
   70.23 +6192	75.7483
   70.24 +6711	88.3167
   70.25 +6973	95.5403
   70.26 +7075	97.3207
   70.27 +7294	103.253
   70.28 +7653	113.638
   70.29 +7869	118.855
   70.30 +7878	119.142
   70.31 +8668	142.724
   70.32 +8726	146.63
   70.33 +9523	171.031
    71.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    71.2 +++ b/randGraph/ind/vf2pInd15_0.7.txt	Tue Nov 22 08:15:16 2016 +0100
    71.3 @@ -0,0 +1,49 @@
    71.4 +115	0.218
    71.5 +197	0.397667
    71.6 +364	0.887
    71.7 +392	1.00033
    71.8 +914	3.32667
    71.9 +950	3.571
   71.10 +1556	7.707
   71.11 +1561	7.97633
   71.12 +1702	9.129
   71.13 +1740	9.286
   71.14 +1834	10.1287
   71.15 +1982	11.714
   71.16 +1998	11.8017
   71.17 +2023	12.0333
   71.18 +2092	12.644
   71.19 +2187	13.815
   71.20 +2297	14.967
   71.21 +2314	15.2977
   71.22 +2399	16.366
   71.23 +2450	16.9767
   71.24 +2534	17.7803
   71.25 +2570	18.3007
   71.26 +2666	19.3383
   71.27 +2712	20.1653
   71.28 +2725	20.0667
   71.29 +2729	20.199
   71.30 +2730	20.3637
   71.31 +2895	22.468
   71.32 +2920	22.8947
   71.33 +2929	22.7347
   71.34 +2997	23.8593
   71.35 +3117	26.0253
   71.36 +3149	26.2507
   71.37 +3182	26.712
   71.38 +3451	30.7967
   71.39 +3464	31.0397
   71.40 +3537	32.0727
   71.41 +3564	32.3637
   71.42 +3594	32.905
   71.43 +3825	37.2367
   71.44 +3892	38.0317
   71.45 +3972	39.4953
   71.46 +4198	44.1937
   71.47 +4243	44.3837
   71.48 +4281	45.103
   71.49 +4327	46.527
   71.50 +4776	55.3963
   71.51 +4882	57.6943
   71.52 +4938	59.1703
    72.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    72.2 +++ b/randGraph/ind/vf2pInd15_0.8.txt	Tue Nov 22 08:15:16 2016 +0100
    72.3 @@ -0,0 +1,30 @@
    72.4 +57	0.116333
    72.5 +864	3.572
    72.6 +1355	7.141
    72.7 +1402	7.623
    72.8 +1580	9.21167
    72.9 +2161	15.619
   72.10 +2295	17.2717
   72.11 +2368	18.1977
   72.12 +2585	21.1427
   72.13 +2720	23.1157
   72.14 +3126	29.6183
   72.15 +3151	30.101
   72.16 +4218	50.8937
   72.17 +4886	66.1663
   72.18 +5022	69.6627
   72.19 +5239	75.1977
   72.20 +5344	77.9527
   72.21 +5361	78.2973
   72.22 +5375	78.8197
   72.23 +5819	91.158
   72.24 +5930	94.378
   72.25 +6273	104.835
   72.26 +6477	111.401
   72.27 +6947	126.704
   72.28 +7598	150.256
   72.29 +8269	175.992
   72.30 +8736	195.773
   72.31 +8868	200.751
   72.32 +8972	205.386
   72.33 +9725	239.337
    73.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    73.2 +++ b/randGraph/ind/vf2pInd15_0.95.txt	Tue Nov 22 08:15:16 2016 +0100
    73.3 @@ -0,0 +1,30 @@
    73.4 +28	0.0666667
    73.5 +322	1.093
    73.6 +449	1.70833
    73.7 +561	2.337
    73.8 +848	4.31167
    73.9 +1519	10.761
   73.10 +2125	18.4883
   73.11 +2211	19.9937
   73.12 +2218	20.0537
   73.13 +2232	20.2807
   73.14 +2533	25.162
   73.15 +2622	26.9303
   73.16 +2892	31.6663
   73.17 +3128	36.231
   73.18 +3156	36.8187
   73.19 +3379	41.4687
   73.20 +3513	44.631
   73.21 +3807	51.283
   73.22 +4061	57.5013
   73.23 +4750	76.1557
   73.24 +4767	76.6803
   73.25 +4768	76.782
   73.26 +5893	112.892
   73.27 +6203	124.273
   73.28 +8331	214.711
   73.29 +8433	220.537
   73.30 +8547	225.248
   73.31 +8935	245.129
   73.32 +9613	281.541
   73.33 +9627	282.218
    74.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    74.2 +++ b/randGraph/ind/vf2pInd32_0.05.txt	Tue Nov 22 08:15:16 2016 +0100
    74.3 @@ -0,0 +1,30 @@
    74.4 +216	0.0483333
    74.5 +407	0.115333
    74.6 +538	0.164667
    74.7 +927	0.400667
    74.8 +1009	0.462333
    74.9 +1277	0.626333
   74.10 +1668	0.952
   74.11 +2391	2.458
   74.12 +3229	2.67367
   74.13 +3754	3.469
   74.14 +3953	4.03
   74.15 +4254	6.02067
   74.16 +4525	4.731
   74.17 +4780	5.11633
   74.18 +5281	8.87567
   74.19 +5861	7.817
   74.20 +6317	8.872
   74.21 +6434	9.72067
   74.22 +6766	18.1203
   74.23 +6881	10.3367
   74.24 +7047	10.7203
   74.25 +7316	11.1883
   74.26 +7396	12.2917
   74.27 +8696	18.3437
   74.28 +8897	59.4683
   74.29 +9051	16.5487
   74.30 +9075	18.851
   74.31 +9377	40.446
   74.32 +9573	26.39
   74.33 +9687	22.042
    75.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    75.2 +++ b/randGraph/ind/vf2pInd32_0.1.txt	Tue Nov 22 08:15:16 2016 +0100
    75.3 @@ -0,0 +1,30 @@
    75.4 +344	0.143667
    75.5 +1434	1.20933
    75.6 +2070	2.17767
    75.7 +2175	2.31733
    75.8 +2480	2.87733
    75.9 +2685	3.26067
   75.10 +3150	4.33467
   75.11 +3611	5.43433
   75.12 +3814	5.951
   75.13 +4085	6.683
   75.14 +4089	6.89333
   75.15 +4565	8.10867
   75.16 +4742	8.58733
   75.17 +4778	8.7
   75.18 +5395	11.0133
   75.19 +5587	11.8337
   75.20 +5598	11.5987
   75.21 +5741	12.2517
   75.22 +6033	13.1647
   75.23 +6357	15.0947
   75.24 +6401	15.002
   75.25 +6581	15.561
   75.26 +6593	15.532
   75.27 +6869	16.6487
   75.28 +7079	17.639
   75.29 +7280	19.2467
   75.30 +7882	21.8247
   75.31 +8847	26.6603
   75.32 +9039	27.7043
   75.33 +9728	32.275
    76.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    76.2 +++ b/randGraph/ind/vf2pInd32_0.3.txt	Tue Nov 22 08:15:16 2016 +0100
    76.3 @@ -0,0 +1,30 @@
    76.4 +262	0.309333
    76.5 +598	0.919333
    76.6 +694	1.15533
    76.7 +722	1.219
    76.8 +752	1.30767
    76.9 +1116	2.30967
   76.10 +1224	2.66167
   76.11 +1293	2.898
   76.12 +1314	2.959
   76.13 +1836	5.00933
   76.14 +3127	12.1287
   76.15 +3213	12.703
   76.16 +3390	13.9413
   76.17 +3613	15.6223
   76.18 +4832	25.7873
   76.19 +5319	30.644
   76.20 +5330	30.6967
   76.21 +5379	31.2433
   76.22 +5394	31.361
   76.23 +5456	32.0347
   76.24 +6354	42.1693
   76.25 +6579	44.9697
   76.26 +6889	48.9497
   76.27 +7096	51.723
   76.28 +8039	65.0997
   76.29 +8436	71.3323
   76.30 +8686	75.3243
   76.31 +9377	86.862
   76.32 +9455	88.1637
   76.33 +9608	90.9447
    77.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    77.2 +++ b/randGraph/ind/vf2pInd32_0.6.txt	Tue Nov 22 08:15:16 2016 +0100
    77.3 @@ -0,0 +1,30 @@
    77.4 +136	0.363333
    77.5 +1037	4.887
    77.6 +1104	5.14633
    77.7 +1198	5.79467
    77.8 +1204	5.89733
    77.9 +1400	7.36467
   77.10 +1533	8.404
   77.11 +1669	9.62233
   77.12 +1723	10.1267
   77.13 +2230	15.155
   77.14 +3701	34.8173
   77.15 +4063	42.5703
   77.16 +4258	43.9077
   77.17 +4476	47.9777
   77.18 +5205	62.309
   77.19 +5304	64.399
   77.20 +5718	73.5017
   77.21 +6123	83.217
   77.22 +6141	83.6287
   77.23 +6192	85.131
   77.24 +6711	97.8737
   77.25 +6973	104.891
   77.26 +7075	107.821
   77.27 +7294	114.304
   77.28 +7653	123.88
   77.29 +7869	132.351
   77.30 +7878	130.796
   77.31 +8668	156.333
   77.32 +8726	158.004
   77.33 +9523	185.501
    78.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    78.2 +++ b/randGraph/ind/vf2pInd32_0.8.txt	Tue Nov 22 08:15:16 2016 +0100
    78.3 @@ -0,0 +1,30 @@
    78.4 +248	1.11367
    78.5 +439	2.172
    78.6 +443	2.244
    78.7 +1328	9.922
    78.8 +1471	11.5383
    78.9 +2396	24.0727
   78.10 +2454	25.0777
   78.11 +2968	33.7757
   78.12 +2997	34.6437
   78.13 +3149	37.539
   78.14 +3328	40.9153
   78.15 +3472	43.9497
   78.16 +3850	52.1813
   78.17 +4055	56.9343
   78.18 +5013	81.4517
   78.19 +5059	83.3097
   78.20 +5663	99.998
   78.21 +5728	102.454
   78.22 +6077	115.204
   78.23 +6448	126.072
   78.24 +6510	126.617
   78.25 +6532	128.346
   78.26 +7140	149.279
   78.27 +7297	155.374
   78.28 +7470	162.685
   78.29 +7628	168.062
   78.30 +8250	195.35
   78.31 +8333	199.957
   78.32 +8834	221.676
   78.33 +9980	280.124
    79.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    79.2 +++ b/randGraph/ind/vf2pInd32_0.95.txt	Tue Nov 22 08:15:16 2016 +0100
    79.3 @@ -0,0 +1,30 @@
    79.4 +28	0.092
    79.5 +322	1.87367
    79.6 +449	2.88
    79.7 +561	3.849
    79.8 +848	6.687
    79.9 +1519	15.3643
   79.10 +2125	24.726
   79.11 +2211	26.4567
   79.12 +2218	27.1653
   79.13 +2232	26.7347
   79.14 +2533	32.6447
   79.15 +2622	33.9373
   79.16 +2892	40.2703
   79.17 +3128	46.1757
   79.18 +3156	46.894
   79.19 +3379	51.711
   79.20 +3513	55.5957
   79.21 +3807	61.8537
   79.22 +4061	70.1517
   79.23 +4750	89.438
   79.24 +4767	89.9523
   79.25 +4768	91.593
   79.26 +5893	129.177
   79.27 +6203	141.726
   79.28 +8331	241.685
   79.29 +8433	253.332
   79.30 +8547	252.701
   79.31 +8935	275.213
   79.32 +9613	317.321
   79.33 +9627	310.94
    80.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    80.2 +++ b/randGraph/ind/vf2pInd35_0.05.txt	Tue Nov 22 08:15:16 2016 +0100
    80.3 @@ -0,0 +1,47 @@
    80.4 +33	0.004
    80.5 +684	0.255333
    80.6 +1057	0.492
    80.7 +1125	0.534667
    80.8 +1578	0.919333
    80.9 +1860	1.234
   80.10 +1867	1.21633
   80.11 +1990	1.263
   80.12 +2036	1.30067
   80.13 +2595	1.94167
   80.14 +2607	1.921
   80.15 +2756	3.03567
   80.16 +3185	2.718
   80.17 +3275	2.70667
   80.18 +3362	3.14733
   80.19 +3466	3.34367
   80.20 +3492	3.081
   80.21 +3564	3.14767
   80.22 +3656	3.34333
   80.23 +3834	3.45633
   80.24 +4345	4.58533
   80.25 +4605	4.69967
   80.26 +4740	5.30433
   80.27 +4921	6.00767
   80.28 +4941	5.772
   80.29 +4993	5.941
   80.30 +5513	7.71433
   80.31 +5767	7.69133
   80.32 +6134	9.76067
   80.33 +6410	9.202
   80.34 +6534	10.31
   80.35 +6904	9.506
   80.36 +7010	11.4237
   80.37 +7067	11.7407
   80.38 +7231	11.6627
   80.39 +7314	13.9493
   80.40 +7525	12.132
   80.41 +7538	12.1363
   80.42 +7660	12.3557
   80.43 +8422	14.5693
   80.44 +8696	81.2783
   80.45 +8885	17.4843
   80.46 +8916	19.0267
   80.47 +8919	16.0893
   80.48 +9337	19.1553
   80.49 +9878	31.0497
   80.50 +9999	19.6727
    81.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    81.2 +++ b/randGraph/ind/vf2pInd35_0.1.txt	Tue Nov 22 08:15:16 2016 +0100
    81.3 @@ -0,0 +1,50 @@
    81.4 +302	0.128333
    81.5 +450	0.220667
    81.6 +697	0.416
    81.7 +744	0.467667
    81.8 +805	0.529333
    81.9 +938	0.661333
   81.10 +963	0.705
   81.11 +1043	0.775333
   81.12 +1240	1.00267
   81.13 +1797	1.827
   81.14 +2018	2.12733
   81.15 +2124	2.32367
   81.16 +2435	2.88867
   81.17 +2810	3.647
   81.18 +3368	4.925
   81.19 +3401	5.17133
   81.20 +3531	5.43567
   81.21 +3674	5.749
   81.22 +3734	5.86533
   81.23 +4359	7.56333
   81.24 +4403	7.76633
   81.25 +4406	7.923
   81.26 +4466	7.878
   81.27 +4579	8.57667
   81.28 +4685	8.60433
   81.29 +4940	9.43967
   81.30 +5007	9.67867
   81.31 +5312	10.7183
   81.32 +5471	11.3373
   81.33 +5564	11.6963
   81.34 +5962	13.1663
   81.35 +6114	14.087
   81.36 +6677	16.2267
   81.37 +7019	17.8927
   81.38 +7128	18.3563
   81.39 +7468	19.748
   81.40 +7488	20.108
   81.41 +7636	21.851
   81.42 +7668	21.656
   81.43 +7823	21.697
   81.44 +8143	23.279
   81.45 +8156	23.6977
   81.46 +8333	24.531
   81.47 +8572	25.7437
   81.48 +8961	27.7373
   81.49 +9009	28.0237
   81.50 +9443	30.8153
   81.51 +9784	32.6847
   81.52 +9868	33.4577
   81.53 +9959	33.867
    82.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    82.2 +++ b/randGraph/ind/vf2pInd35_0.3.txt	Tue Nov 22 08:15:16 2016 +0100
    82.3 @@ -0,0 +1,50 @@
    82.4 +326	0.440667
    82.5 +399	0.560333
    82.6 +476	0.708667
    82.7 +1069	2.27567
    82.8 +1389	3.39033
    82.9 +1415	3.508
   82.10 +1654	4.47167
   82.11 +1909	5.48733
   82.12 +1961	5.76733
   82.13 +2638	9.36833
   82.14 +3005	11.6703
   82.15 +3045	12.1313
   82.16 +3144	12.635
   82.17 +3229	13.213
   82.18 +3275	13.6237
   82.19 +3803	17.1753
   82.20 +4459	23.0647
   82.21 +4816	26.3773
   82.22 +4988	27.9623
   82.23 +5097	28.998
   82.24 +5424	32.519
   82.25 +5465	32.8147
   82.26 +5634	34.8827
   82.27 +5645	34.648
   82.28 +6022	39.1953
   82.29 +6094	40.01
   82.30 +6159	40.5813
   82.31 +6291	42.185
   82.32 +6361	43.3303
   82.33 +6638	47.9383
   82.34 +6677	47.2617
   82.35 +6838	48.9613
   82.36 +7043	52.919
   82.37 +7531	58.8037
   82.38 +7566	59.2117
   82.39 +7623	59.7657
   82.40 +7647	60.3467
   82.41 +7822	62.6957
   82.42 +7994	65.3453
   82.43 +8003	65.7403
   82.44 +8475	73.3503
   82.45 +8996	85.0193
   82.46 +9118	83.9353
   82.47 +9256	87.1167
   82.48 +9702	93.593
   82.49 +9750	94.753
   82.50 +9753	94.6723
   82.51 +9787	95.2873
   82.52 +9848	96.5613
   82.53 +9849	99.8623
    83.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    83.2 +++ b/randGraph/ind/vf2pInd35_0.6.txt	Tue Nov 22 08:15:16 2016 +0100
    83.3 @@ -0,0 +1,50 @@
    83.4 +379	1.304
    83.5 +431	1.55767
    83.6 +665	2.743
    83.7 +718	2.95
    83.8 +826	3.58
    83.9 +1251	6.52667
   83.10 +1279	6.73867
   83.11 +1443	8.25133
   83.12 +1500	8.65767
   83.13 +2193	15.2023
   83.14 +2231	15.5933
   83.15 +2280	16.1503
   83.16 +2632	20.2637
   83.17 +2687	21.059
   83.18 +2907	23.782
   83.19 +3053	25.886
   83.20 +3091	26.434
   83.21 +3437	31.5983
   83.22 +3587	34.2333
   83.23 +3976	39.9213
   83.24 +4702	53.383
   83.25 +4751	54.564
   83.26 +5349	67.4433
   83.27 +5350	67.262
   83.28 +5353	67.505
   83.29 +5722	74.9237
   83.30 +5764	76.005
   83.31 +5844	77.7597
   83.32 +5946	80.0777
   83.33 +5969	80.8947
   83.34 +5993	81.0297
   83.35 +6013	81.995
   83.36 +6323	89.7763
   83.37 +6883	104.332
   83.38 +6917	105.1
   83.39 +7218	113.653
   83.40 +7383	120.002
   83.41 +7663	127.383
   83.42 +8038	138.808
   83.43 +8119	140.824
   83.44 +8133	140.531
   83.45 +8165	142.339
   83.46 +8204	144.491
   83.47 +8694	158.751
   83.48 +8805	164.991
   83.49 +9262	180.528
   83.50 +9334	182.775
   83.51 +9569	189.227
   83.52 +9811	198.952
   83.53 +9876	202.732
    84.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    84.2 +++ b/randGraph/ind/vf2pInd35_0.8.txt	Tue Nov 22 08:15:16 2016 +0100
    84.3 @@ -0,0 +1,50 @@
    84.4 +22	0.045
    84.5 +155	0.700333
    84.6 +176	0.784333
    84.7 +911	6.20033
    84.8 +1065	7.59467
    84.9 +1107	8.02367
   84.10 +1526	13.3993
   84.11 +1623	13.9763
   84.12 +1782	15.9207
   84.13 +1863	16.9817
   84.14 +1911	17.7677
   84.15 +2165	22.11
   84.16 +2192	22.0237
   84.17 +2217	22.17
   84.18 +2247	22.46
   84.19 +3050	36.9757
   84.20 +3167	39.482
   84.21 +3398	45.8423
   84.22 +3627	47.983
   84.23 +4092	60.179
   84.24 +4240	62.5573
   84.25 +4346	65.6493
   84.26 +4615	72.9677
   84.27 +4673	75.9043
   84.28 +4708	76.1693
   84.29 +4739	75.6093
   84.30 +4818	78.779
   84.31 +5058	85.1967
   84.32 +5222	88.906
   84.33 +5414	95.2437
   84.34 +5868	109.191
   84.35 +5946	116.128
   84.36 +6061	115.374
   84.37 +6263	122.258
   84.38 +6611	136.819
   84.39 +6699	138.081
   84.40 +6799	141.604
   84.41 +6915	146.624
   84.42 +7100	152.956
   84.43 +7136	154.626
   84.44 +7218	157.368
   84.45 +7369	167.007
   84.46 +7736	180.202
   84.47 +8219	199.971
   84.48 +8377	210.541
   84.49 +8482	214.688
   84.50 +8632	217.674
   84.51 +8886	234.622
   84.52 +9351	251.814
   84.53 +9771	284.116
    85.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    85.2 +++ b/randGraph/ind/vf2pInd35_0.95.txt	Tue Nov 22 08:15:16 2016 +0100
    85.3 @@ -0,0 +1,49 @@
    85.4 +20	0.049
    85.5 +550	3.94
    85.6 +628	4.72633
    85.7 +660	5.01467
    85.8 +1192	11.1367
    85.9 +1663	18.0227
   85.10 +1749	20.1853
   85.11 +1768	19.665
   85.12 +2082	24.8423
   85.13 +2355	31.2503
   85.14 +2375	30.2203
   85.15 +2617	35.2503
   85.16 +2946	43.0043
   85.17 +3499	56.9613
   85.18 +3567	58.4403
   85.19 +3774	67.8443
   85.20 +3923	68.45
   85.21 +4002	71.0137
   85.22 +4189	75.521
   85.23 +4205	79.518
   85.24 +4214	77.788
   85.25 +4414	81.9137
   85.26 +4430	82.603
   85.27 +4481	84.3963
   85.28 +4500	86.8007
   85.29 +4706	92.226
   85.30 +4861	97.081
   85.31 +5162	107.331
   85.32 +5650	126.66
   85.33 +5724	128.453
   85.34 +5795	130.164
   85.35 +5938	138.769
   85.36 +5944	137.439
   85.37 +6006	140.665
   85.38 +6057	147.517
   85.39 +6462	161.468
   85.40 +6536	162.08
   85.41 +6668	170.276
   85.42 +6996	188.282
   85.43 +7594	213.816
   85.44 +7936	230.678
   85.45 +8716	269.054
   85.46 +8871	271.437
   85.47 +9032	283.079
   85.48 +9142	292.064
   85.49 +9164	311.828
   85.50 +9435	308.418
   85.51 +9465	320.903
   85.52 +9792	341.184
    86.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    86.2 +++ b/randGraph/ind/vf2pInd5_0.05.txt	Tue Nov 22 08:15:16 2016 +0100
    86.3 @@ -0,0 +1,50 @@
    86.4 +354	0.042
    86.5 +446	0.061
    86.6 +631	0.104333
    86.7 +668	0.109667
    86.8 +842	0.164667
    86.9 +1296	0.334
   86.10 +1327	0.354
   86.11 +1495	0.424333
   86.12 +1713	0.554667
   86.13 +2027	0.735333
   86.14 +2106	0.802667
   86.15 +2901	1.459
   86.16 +2967	1.494
   86.17 +3169	1.79833
   86.18 +3279	1.942
   86.19 +3320	1.84067
   86.20 +3510	2.026
   86.21 +4337	3.03467
   86.22 +4535	3.29267
   86.23 +4841	3.747
   86.24 +5020	4.00767
   86.25 +5111	4.14067
   86.26 +5163	4.54733
   86.27 +5359	4.85367
   86.28 +5542	4.838
   86.29 +5547	4.852
   86.30 +5562	4.86767
   86.31 +5631	4.97333
   86.32 +5877	5.41667
   86.33 +6101	5.932
   86.34 +6295	6.19133
   86.35 +6584	6.75567
   86.36 +6594	6.82033
   86.37 +6788	7.783
   86.38 +6849	7.599
   86.39 +7173	7.93133
   86.40 +7279	8.18833
   86.41 +7361	8.36933
   86.42 +7384	8.44133
   86.43 +7461	8.64567
   86.44 +7467	8.59167
   86.45 +8091	10.7283
   86.46 +8451	10.8843
   86.47 +8827	11.8837
   86.48 +9031	12.6497
   86.49 +9134	12.8663
   86.50 +9427	13.48
   86.51 +9639	14.1477
   86.52 +9720	14.3067
   86.53 +9943	15.8237
    87.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    87.2 +++ b/randGraph/ind/vf2pInd5_0.1.txt	Tue Nov 22 08:15:16 2016 +0100
    87.3 @@ -0,0 +1,48 @@
    87.4 +70	0.00966667
    87.5 +377	0.0856667
    87.6 +390	0.0933333
    87.7 +788	0.266
    87.8 +1086	0.467667
    87.9 +1922	1.274
   87.10 +2057	1.459
   87.11 +2071	1.478
   87.12 +2169	1.685
   87.13 +2406	1.94833
   87.14 +2958	2.95933
   87.15 +3323	3.57
   87.16 +3631	4.21967
   87.17 +4224	6.24633
   87.18 +4380	6.09633
   87.19 +4427	6.37467
   87.20 +4663	7.27233
   87.21 +4942	7.83867
   87.22 +5118	8.14933
   87.23 +5183	8.36267
   87.24 +5204	8.44867
   87.25 +5368	8.984
   87.26 +5704	10.0917
   87.27 +5826	10.6517
   87.28 +5859	10.569
   87.29 +5925	10.901
   87.30 +5948	11.0407
   87.31 +5961	11.743
   87.32 +6052	11.4887
   87.33 +6472	15.3517
   87.34 +6871	14.5153
   87.35 +7015	18.134
   87.36 +7039	15.1717
   87.37 +7221	17.014
   87.38 +7238	17.9207
   87.39 +7776	18.545
   87.40 +7806	18.5313
   87.41 +8478	22.436
   87.42 +8679	22.8333
   87.43 +8966	24.7707
   87.44 +9251	25.9987
   87.45 +9336	27.0017
   87.46 +9499	29.525
   87.47 +9583	27.9523
   87.48 +9585	34.779
   87.49 +9649	77.52
   87.50 +9816	30.638
   87.51 +9932	30.6913
    88.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    88.2 +++ b/randGraph/ind/vf2pInd5_0.3.txt	Tue Nov 22 08:15:16 2016 +0100
    88.3 @@ -0,0 +1,49 @@
    88.4 +326	0.199
    88.5 +399	0.267333
    88.6 +476	0.353333
    88.7 +1069	1.362
    88.8 +1389	2.15067
    88.9 +1415	2.15767
   88.10 +1654	2.86733
   88.11 +1909	3.84733
   88.12 +1961	3.961
   88.13 +2638	6.87267
   88.14 +3005	8.70933
   88.15 +3045	8.90867
   88.16 +3144	9.68167
   88.17 +3229	9.952
   88.18 +3275	10.5163
   88.19 +3803	13.5883
   88.20 +4459	19.0313
   88.21 +4816	21.531
   88.22 +4988	23.239
   88.23 +5097	24.4823
   88.24 +5424	28.021
   88.25 +5465	27.2663
   88.26 +5634	29.8707
   88.27 +5645	29.3437
   88.28 +6022	33
   88.29 +6094	33.717
   88.30 +6159	35.262
   88.31 +6291	36.5397
   88.32 +6361	37.286
   88.33 +6638	40.641
   88.34 +6677	41.6727
   88.35 +6838	42.07
   88.36 +7043	45.2177
   88.37 +7531	52.6313
   88.38 +7566	53.4523
   88.39 +7623	52.2727
   88.40 +7647	52.8467
   88.41 +7822	71.1413
   88.42 +7994	59.2187
   88.43 +8003	59.824
   88.44 +8475	65.147
   88.45 +8996	73.607
   88.46 +9118	76.1177
   88.47 +9256	81.6237
   88.48 +9750	87.1797
   88.49 +9753	91.3717
   88.50 +9787	91.8217
   88.51 +9848	86.729
   88.52 +9849	87.4
    89.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    89.2 +++ b/randGraph/ind/vf2pInd5_0.6.txt	Tue Nov 22 08:15:16 2016 +0100
    89.3 @@ -0,0 +1,50 @@
    89.4 +379	0.494667
    89.5 +431	0.605667
    89.6 +665	1.189
    89.7 +718	1.341
    89.8 +826	1.708
    89.9 +1251	3.50233
   89.10 +1279	3.631
   89.11 +1443	4.50667
   89.12 +1500	4.84533
   89.13 +2193	9.664
   89.14 +2231	10.0093
   89.15 +2280	10.4237
   89.16 +2632	13.5977
   89.17 +2687	14.1333
   89.18 +2907	16.407
   89.19 +3053	18.0413
   89.20 +3091	18.4913
   89.21 +3437	22.572
   89.22 +3587	24.5313
   89.23 +3976	29.7623
   89.24 +4702	41
   89.25 +4751	41.851
   89.26 +5349	52.6303
   89.27 +5350	52.5897
   89.28 +5353	52.5687
   89.29 +5722	59.825
   89.30 +5764	60.897
   89.31 +5844	62.9263
   89.32 +5946	64.5117
   89.33 +5969	64.9087
   89.34 +5993	65.7193
   89.35 +6013	65.8873
   89.36 +6323	72.5703
   89.37 +6883	85.8193
   89.38 +6917	86.475
   89.39 +7218	93.9543
   89.40 +7383	98.1227
   89.41 +7663	105.505
   89.42 +8038	115.815
   89.43 +8119	117.976
   89.44 +8133	118.325
   89.45 +8165	119.396
   89.46 +8204	120.515
   89.47 +8694	134.9
   89.48 +8805	138.845
   89.49 +9262	152.516
   89.50 +9334	156.444
   89.51 +9569	164.193
   89.52 +9811	170.963
   89.53 +9876	172.89
    90.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    90.2 +++ b/randGraph/ind/vf2pInd5_0.8.txt	Tue Nov 22 08:15:16 2016 +0100
    90.3 @@ -0,0 +1,50 @@
    90.4 +22	0.0186667
    90.5 +155	0.201333
    90.6 +176	0.222667
    90.7 +911	2.74667
    90.8 +1065	3.56667
    90.9 +1107	3.82
   90.10 +1526	6.75067
   90.11 +1623	7.55467
   90.12 +1782	8.96033
   90.13 +1863	9.66833
   90.14 +1911	10.1757
   90.15 +2165	12.923
   90.16 +2192	13.0273
   90.17 +2217	13.338
   90.18 +2247	13.6367
   90.19 +3050	24.2777
   90.20 +3167	26.036
   90.21 +3398	29.746
   90.22 +3627	33.5413
   90.23 +4092	42.2407
   90.24 +4240	45.1543
   90.25 +4346	48.223
   90.26 +4615	53.2423
   90.27 +4673	54.4743
   90.28 +4708	55.3837
   90.29 +4739	56.768
   90.30 +4818	57.6567
   90.31 +5058	63.4033
   90.32 +5222	67.2153
   90.33 +5414	72.2027
   90.34 +5868	84.217
   90.35 +5946	86.786
   90.36 +6061	89.7137
   90.37 +6263	95.571
   90.38 +6611	106.224
   90.39 +6699	108.918
   90.40 +6799	112.146
   90.41 +6915	115.882
   90.42 +7100	122.037
   90.43 +7136	123.168
   90.44 +7218	126.608
   90.45 +7369	131.009
   90.46 +7736	143.94
   90.47 +8219	161.959
   90.48 +8377	167.891
   90.49 +8482	172.541
   90.50 +8632	179.712
   90.51 +8886	188.364
   90.52 +9351	208.154
   90.53 +9771	227.267
    91.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    91.2 +++ b/randGraph/ind/vf2pInd5_0.95.txt	Tue Nov 22 08:15:16 2016 +0100
    91.3 @@ -0,0 +1,49 @@
    91.4 +20	0.02
    91.5 +550	1.45267
    91.6 +628	1.793
    91.7 +660	1.923
    91.8 +1192	5.2
    91.9 +1663	9.43367
   91.10 +1749	10.3543
   91.11 +1768	10.5797
   91.12 +2082	14.1837
   91.13 +2355	17.9237
   91.14 +2375	18.6123
   91.15 +2617	21.9483
   91.16 +2946	27.5247
   91.17 +3499	37.583
   91.18 +3567	38.9343
   91.19 +3774	43.5577
   91.20 +3923	46.8577
   91.21 +4002	48.6863
   91.22 +4189	52.968
   91.23 +4205	53.1783
   91.24 +4214	53.656
   91.25 +4414	58.3077
   91.26 +4430	58.6777
   91.27 +4481	59.972
   91.28 +4500	60.5043
   91.29 +4706	66.548
   91.30 +4861	70.1353
   91.31 +5162	78.8657
   91.32 +5650	96.785
   91.33 +5724	95.6887
   91.34 +5795	98.4357
   91.35 +5938	103.126
   91.36 +5944	103.095
   91.37 +6006	105.139
   91.38 +6057	107.132
   91.39 +6462	121.897
   91.40 +6536	123.841
   91.41 +6668	131.597
   91.42 +6996	141.533
   91.43 +7594	166.466
   91.44 +7936	180.745
   91.45 +8716	216.966
   91.46 +8871	223.681
   91.47 +9032	232.128
   91.48 +9142	237.983
   91.49 +9164	239.712
   91.50 +9435	252.498
   91.51 +9465	255.209
   91.52 +9792	272.201
    92.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    92.2 +++ b/randGraph/ind/vf2pInd7_0.05.txt	Tue Nov 22 08:15:16 2016 +0100
    92.3 @@ -0,0 +1,30 @@
    92.4 +78	0.00633333
    92.5 +104	0.00966667
    92.6 +132	0.012
    92.7 +142	0.0156667
    92.8 +173	0.0166667
    92.9 +196	0.0213333
   92.10 +218	0.0236667
   92.11 +276	0.0323333
   92.12 +293	0.0353333
   92.13 +296	0.0353333
   92.14 +366	0.049
   92.15 +423	0.0603333
   92.16 +458	0.067
   92.17 +460	0.0693333
   92.18 +486	0.073
   92.19 +561	0.095
   92.20 +575	0.0953333
   92.21 +641	0.118333
   92.22 +792	0.153333
   92.23 +870	0.178
   92.24 +922	0.206667
   92.25 +992	0.236333
   92.26 +1114	0.267667
   92.27 +1166	0.292667
   92.28 +1202	0.311667
   92.29 +1608	0.505333
   92.30 +1737	0.573667
   92.31 +2022	0.802333
   92.32 +2837	1.41533
   92.33 +3271	1.84667
    93.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    93.2 +++ b/randGraph/ind/vf2pInd7_0.1.txt	Tue Nov 22 08:15:16 2016 +0100
    93.3 @@ -0,0 +1,30 @@
    93.4 +47	0.006
    93.5 +85	0.013
    93.6 +150	0.0256667
    93.7 +192	0.0356667
    93.8 +200	0.037
    93.9 +206	0.038
   93.10 +273	0.0563333
   93.11 +302	0.0693333
   93.12 +387	0.092
   93.13 +394	0.0936667
   93.14 +536	0.153333
   93.15 +790	0.282667
   93.16 +816	0.311
   93.17 +851	0.331333
   93.18 +925	0.374
   93.19 +1085	0.483333
   93.20 +1107	0.496667
   93.21 +1135	0.516667
   93.22 +1460	0.847
   93.23 +1488	0.869667
   93.24 +1954	1.39833
   93.25 +2054	1.51533
   93.26 +2170	1.729
   93.27 +2190	1.67733
   93.28 +2253	2.786
   93.29 +2257	1.77167
   93.30 +2311	1.90167
   93.31 +2390	2.02967
   93.32 +2463	2.083
   93.33 +3366	3.765
    94.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    94.2 +++ b/randGraph/ind/vf2pInd7_0.3.txt	Tue Nov 22 08:15:16 2016 +0100
    94.3 @@ -0,0 +1,28 @@
    94.4 +20	0.00666667
    94.5 +47	0.0176667
    94.6 +65	0.0256667
    94.7 +82	0.0366667
    94.8 +85	0.0346667
    94.9 +101	0.0453333
   94.10 +141	0.0666667
   94.11 +213	0.116667
   94.12 +228	0.123333
   94.13 +272	0.162667
   94.14 +277	0.172333
   94.15 +355	0.238333
   94.16 +491	0.382333
   94.17 +587	0.505
   94.18 +654	0.601667
   94.19 +698	0.673
   94.20 +716	0.703333
   94.21 +763	0.779
   94.22 +851	0.970333
   94.23 +1032	1.29067
   94.24 +1095	1.421
   94.25 +1603	2.78933
   94.26 +1969	4.05133
   94.27 +2176	4.86067
   94.28 +2412	5.86433
   94.29 +2587	6.67967
   94.30 +2958	8.63433
   94.31 +4266	17.2513
    95.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    95.2 +++ b/randGraph/ind/vf2pInd7_0.6.txt	Tue Nov 22 08:15:16 2016 +0100
    95.3 @@ -0,0 +1,29 @@
    95.4 +20	0.0176667
    95.5 +25	0.0193333
    95.6 +43	0.0386667
    95.7 +56	0.0516667
    95.8 +227	0.266667
    95.9 +397	0.587333
   95.10 +448	0.698
   95.11 +474	0.769
   95.12 +487	0.795
   95.13 +509	0.849333
   95.14 +630	1.18
   95.15 +727	1.50333
   95.16 +732	1.52167
   95.17 +777	1.68267
   95.18 +826	1.83933
   95.19 +899	2.108
   95.20 +1034	2.67733
   95.21 +1078	2.85433
   95.22 +1107	3.00767
   95.23 +1146	3.19433
   95.24 +1282	3.90833
   95.25 +1393	4.439
   95.26 +1410	4.676
   95.27 +1484	5.00367
   95.28 +1600	5.71033
   95.29 +2053	8.91533
   95.30 +2076	9.08333
   95.31 +2201	10.1147
   95.32 +2813	15.9103
    96.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    96.2 +++ b/randGraph/ind/vf2pInd7_0.8.txt	Tue Nov 22 08:15:16 2016 +0100
    96.3 @@ -0,0 +1,30 @@
    96.4 +37	0.0423333
    96.5 +70	0.0863333
    96.6 +157	0.238
    96.7 +199	0.322
    96.8 +271	0.468
    96.9 +376	0.770333
   96.10 +379	0.77
   96.11 +380	0.774333
   96.12 +522	1.24
   96.13 +554	1.35333
   96.14 +595	1.523
   96.15 +634	1.652
   96.16 +718	2.018
   96.17 +721	2.04067
   96.18 +730	2.07067
   96.19 +928	3.07467
   96.20 +1046	3.753
   96.21 +1088	3.99333
   96.22 +1156	4.42567
   96.23 +1357	5.83733
   96.24 +1443	6.48867
   96.25 +1564	7.486
   96.26 +1579	7.59033
   96.27 +1780	9.42333
   96.28 +1860	10.198
   96.29 +1876	10.3787
   96.30 +2079	12.4097
   96.31 +2866	22.3363
   96.32 +3318	29.3473
   96.33 +4068	43.058
    97.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    97.2 +++ b/randGraph/ind/vf2pInd7_0.95.txt	Tue Nov 22 08:15:16 2016 +0100
    97.3 @@ -0,0 +1,28 @@
    97.4 +20	0.0326667
    97.5 +59	0.0956667
    97.6 +80	0.136333
    97.7 +108	0.180667
    97.8 +166	0.342667
    97.9 +176	0.353667
   97.10 +222	0.465333
   97.11 +444	1.221
   97.12 +624	1.98067
   97.13 +631	2.01
   97.14 +669	2.198
   97.15 +757	2.66133
   97.16 +876	3.37067
   97.17 +891	3.45033
   97.18 +1124	5.10967
   97.19 +1193	5.64333
   97.20 +1217	5.91667
   97.21 +1345	6.93567
   97.22 +1449	7.88367
   97.23 +1603	9.44067
   97.24 +1655	9.98667
   97.25 +2079	15.527
   97.26 +2129	15.7007
   97.27 +2567	21.9067
   97.28 +2716	24.4203
   97.29 +3103	31.128
   97.30 +3657	42.242
   97.31 +4945	74.4017
    98.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    98.2 +++ b/randGraph/ind/vf2ppInd10_0.05.txt	Tue Nov 22 08:15:16 2016 +0100
    98.3 @@ -0,0 +1,50 @@
    98.4 +354	0.0213333
    98.5 +446	0.029
    98.6 +631	0.044
    98.7 +668	0.043
    98.8 +842	0.062
    98.9 +1296	0.0866667
   98.10 +1327	0.0963333
   98.11 +1495	0.105
   98.12 +1713	0.128
   98.13 +2027	0.129333
   98.14 +2106	0.172
   98.15 +2901	0.207333
   98.16 +2967	0.235
   98.17 +3169	0.313333
   98.18 +3279	1.13867
   98.19 +3320	0.268333
   98.20 +3510	0.271333
   98.21 +4337	0.383
   98.22 +4535	0.784333
   98.23 +4841	0.376
   98.24 +5020	11.99
   98.25 +5111	0.631333
   98.26 +5163	0.456
   98.27 +5359	0.532
   98.28 +5542	0.409
   98.29 +5547	0.390667
   98.30 +5562	1.90533
   98.31 +5631	1.079
   98.32 +5877	0.505333
   98.33 +6101	0.489667
   98.34 +6295	0.470333
   98.35 +6584	2.44433
   98.36 +6594	19.3737
   98.37 +6788	2.752
   98.38 +6849	0.527333
   98.39 +7173	1.077
   98.40 +7279	2.22867
   98.41 +7361	0.739667
   98.42 +7384	2.746
   98.43 +7461	127.963
   98.44 +7467	1.13867
   98.45 +8091	1.29667
   98.46 +8451	0.656667
   98.47 +8827	66.1093
   98.48 +9031	0.911667
   98.49 +9134	20.6043
   98.50 +9427	0.798
   98.51 +9639	1.06033
   98.52 +9720	5.394
   98.53 +9943	1.997
    99.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    99.2 +++ b/randGraph/ind/vf2ppInd10_0.1.txt	Tue Nov 22 08:15:16 2016 +0100
    99.3 @@ -0,0 +1,48 @@
    99.4 +70	0.008
    99.5 +377	0.0476667
    99.6 +390	0.0596667
    99.7 +788	0.116667
    99.8 +1086	0.154333
    99.9 +1922	0.260333
   99.10 +2057	0.265667
   99.11 +2071	0.306333
   99.12 +2169	0.358333
   99.13 +2406	0.573667
   99.14 +2958	0.496333
   99.15 +3323	1.10033
   99.16 +3631	0.498333
   99.17 +4224	2.97633
   99.18 +4380	1.394
   99.19 +4427	1.05067
   99.20 +4663	1.098
   99.21 +4942	1.568
   99.22 +5118	0.946667
   99.23 +5183	0.800667
   99.24 +5204	1.32433
   99.25 +5368	1.427
   99.26 +5704	1.175
   99.27 +5826	1.62467
   99.28 +5859	1.14
   99.29 +5925	5.22067
   99.30 +5948	5.151
   99.31 +5961	2.336
   99.32 +6052	7.86367
   99.33 +6472	4.58433
   99.34 +6871	5.176
   99.35 +7015	2.91567
   99.36 +7039	1.56433
   99.37 +7221	5.88167
   99.38 +7238	1.15867
   99.39 +7776	3.652
   99.40 +7806	11.2547
   99.41 +8478	14.108
   99.42 +8679	9.199
   99.43 +8966	8.07367
   99.44 +9251	36.0683
   99.45 +9336	3.62633
   99.46 +9499	40.213
   99.47 +9583	11.5847
   99.48 +9585	5.372
   99.49 +9649	499.196
   99.50 +9816	19.6343
   99.51 +9932	3.18467
   100.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   100.2 +++ b/randGraph/ind/vf2ppInd10_0.3.txt	Tue Nov 22 08:15:16 2016 +0100
   100.3 @@ -0,0 +1,50 @@
   100.4 +326	0.122667
   100.5 +399	0.158
   100.6 +476	0.19
   100.7 +1069	0.440333
   100.8 +1389	0.578
   100.9 +1415	0.588
  100.10 +1654	0.699333
  100.11 +1909	0.830667
  100.12 +1961	0.811333
  100.13 +2638	1.361
  100.14 +3005	1.39367
  100.15 +3045	1.407
  100.16 +3144	1.42767
  100.17 +3229	1.69733
  100.18 +3275	1.49733
  100.19 +3803	1.963
  100.20 +4459	2.233
  100.21 +4816	2.28267
  100.22 +4988	2.47933
  100.23 +5097	2.67933
  100.24 +5424	2.91633
  100.25 +5465	2.99933
  100.26 +5634	3.07333
  100.27 +5645	3.224
  100.28 +6022	2.97333
  100.29 +6094	3.03967
  100.30 +6159	3.767
  100.31 +6291	2.952
  100.32 +6361	2.99367
  100.33 +6638	4.44067
  100.34 +6677	3.07867
  100.35 +6838	4.14167
  100.36 +7043	4.32567
  100.37 +7531	3.77567
  100.38 +7566	3.97833
  100.39 +7623	4.11233
  100.40 +7647	4.552
  100.41 +7822	4.82467
  100.42 +7994	4.35267
  100.43 +8003	4.042
  100.44 +8475	4.786
  100.45 +8996	4.78967
  100.46 +9118	5.09367
  100.47 +9256	5.06733
  100.48 +9702	6.66567
  100.49 +9750	5.32933
  100.50 +9753	6.09333
  100.51 +9787	5.00067
  100.52 +9848	6.21267
  100.53 +9849	5.135
   101.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   101.2 +++ b/randGraph/ind/vf2ppInd10_0.6.txt	Tue Nov 22 08:15:16 2016 +0100
   101.3 @@ -0,0 +1,50 @@
   101.4 +379	0.363667
   101.5 +431	0.392333
   101.6 +665	0.625
   101.7 +718	0.686333
   101.8 +826	0.797333
   101.9 +1251	1.23167
  101.10 +1279	1.29267
  101.11 +1443	1.50733
  101.12 +1500	1.52067
  101.13 +2193	2.234
  101.14 +2231	2.262
  101.15 +2280	2.35133
  101.16 +2632	2.76867
  101.17 +2687	2.781
  101.18 +2907	3.16533
  101.19 +3053	3.29767
  101.20 +3091	3.36433
  101.21 +3437	3.69
  101.22 +3587	3.81933
  101.23 +3976	4.31133
  101.24 +4702	5.154
  101.25 +4751	5.19467
  101.26 +5349	5.89933
  101.27 +5350	5.955
  101.28 +5353	5.91467
  101.29 +5722	6.85567
  101.30 +5764	6.48367
  101.31 +5844	6.50733
  101.32 +5946	6.64233
  101.33 +5969	6.803
  101.34 +5993	6.76567
  101.35 +6013	6.766
  101.36 +6323	7.207
  101.37 +6883	8.03367
  101.38 +6917	7.98533
  101.39 +7218	8.47467
  101.40 +7383	8.57
  101.41 +7663	8.92767
  101.42 +8038	9.49367
  101.43 +8119	9.51667
  101.44 +8133	10.128
  101.45 +8165	9.59467
  101.46 +8204	9.61967
  101.47 +8694	10.1283
  101.48 +8805	10.378
  101.49 +9262	10.8383
  101.50 +9334	10.9447
  101.51 +9569	11.28
  101.52 +9811	11.663
  101.53 +9876	11.675
   102.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   102.2 +++ b/randGraph/ind/vf2ppInd10_0.8.txt	Tue Nov 22 08:15:16 2016 +0100
   102.3 @@ -0,0 +1,50 @@
   102.4 +22	0.0266667
   102.5 +155	0.21
   102.6 +176	0.236667
   102.7 +911	1.297
   102.8 +1065	1.57533
   102.9 +1107	1.61733
  102.10 +1526	2.259
  102.11 +1623	2.48567
  102.12 +1782	2.81767
  102.13 +1863	2.838
  102.14 +1911	2.89667
  102.15 +2165	3.31867
  102.16 +2192	3.348
  102.17 +2217	3.445
  102.18 +2247	3.59367
  102.19 +3050	4.935
  102.20 +3167	5.151
  102.21 +3398	5.51833
  102.22 +3627	5.90267
  102.23 +4092	6.87
  102.24 +4240	7.22467
  102.25 +4346	7.32867
  102.26 +4615	7.695
  102.27 +4673	7.90567
  102.28 +4708	7.988
  102.29 +4739	8.083
  102.30 +4818	8.18833
  102.31 +5058	8.73
  102.32 +5222	9.14267
  102.33 +5414	9.27467
  102.34 +5868	10.5013
  102.35 +5946	10.2697
  102.36 +6061	10.8493
  102.37 +6263	11.3743
  102.38 +6611	11.4547
  102.39 +6699	11.75
  102.40 +6799	12.2597
  102.41 +6915	12.1893
  102.42 +7100	12.796
  102.43 +7136	12.5183
  102.44 +7218	12.9163
  102.45 +7369	13.036
  102.46 +7736	13.905
  102.47 +8219	14.67
  102.48 +8377	15.2837
  102.49 +8482	15.0247
  102.50 +8632	15.2837
  102.51 +8886	15.868
  102.52 +9351	16.7927
  102.53 +9771	17.4753
   103.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   103.2 +++ b/randGraph/ind/vf2ppInd10_0.95.txt	Tue Nov 22 08:15:16 2016 +0100
   103.3 @@ -0,0 +1,39 @@
   103.4 +550	0.977333
   103.5 +628	1.12967
   103.6 +660	1.16167
   103.7 +1192	2.21433
   103.8 +1663	3.18033
   103.9 +1749	3.43967
  103.10 +2082	4.02067
  103.11 +2355	4.75233
  103.12 +2375	4.75433
  103.13 +2946	6.37567
  103.14 +3499	7.39967
  103.15 +3567	7.56767
  103.16 +3774	8.10367
  103.17 +4189	9.01667
  103.18 +4205	9.05533
  103.19 +4214	9.09067
  103.20 +4414	9.57467
  103.21 +4430	10.0363
  103.22 +4481	9.95667
  103.23 +4500	9.74033
  103.24 +4861	10.8177
  103.25 +5162	11.4517
  103.26 +5650	12.598
  103.27 +5724	13.0937
  103.28 +5795	13.2703
  103.29 +5944	13.2853
  103.30 +6006	13.8167
  103.31 +6057	13.4997
  103.32 +6462	14.4263
  103.33 +6536	14.7693
  103.34 +6668	15.2183
  103.35 +6996	15.9877
  103.36 +7594	17.3567
  103.37 +7936	18.2223
  103.38 +8716	20.4137
  103.39 +9142	21.4613
  103.40 +9164	21.742
  103.41 +9435	21.7353
  103.42 +9465	22.3537
   104.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   104.2 +++ b/randGraph/ind/vf2ppInd15_0.05.txt	Tue Nov 22 08:15:16 2016 +0100
   104.3 @@ -0,0 +1,30 @@
   104.4 +216	0.0146667
   104.5 +407	0.0306667
   104.6 +538	0.0413333
   104.7 +927	0.0796667
   104.8 +1009	0.0803333
   104.9 +1277	0.0966667
  104.10 +1668	0.133667
  104.11 +2391	0.220667
  104.12 +3229	0.483667
  104.13 +3754	0.379
  104.14 +3953	0.362333
  104.15 +4254	0.448333
  104.16 +4525	0.44
  104.17 +4780	0.854
  104.18 +5281	1.765
  104.19 +5861	1.72167
  104.20 +6317	28.055
  104.21 +6434	8.12967
  104.22 +6766	0.83
  104.23 +6881	4.948
  104.24 +7047	1.42567
  104.25 +7316	20.8757
  104.26 +7396	4.272
  104.27 +8696	45.728
  104.28 +8897	3.91867
  104.29 +9051	22.0687
  104.30 +9075	47.6293
  104.31 +9377	33.6793
  104.32 +9573	5.967
  104.33 +9687	56.9007
   105.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   105.2 +++ b/randGraph/ind/vf2ppInd15_0.1.txt	Tue Nov 22 08:15:16 2016 +0100
   105.3 @@ -0,0 +1,30 @@
   105.4 +344	0.0553333
   105.5 +1434	0.264
   105.6 +2070	0.424333
   105.7 +2175	0.442333
   105.8 +2480	0.467333
   105.9 +2685	0.545
  105.10 +3150	0.735333
  105.11 +3611	0.881
  105.12 +3814	1.27267
  105.13 +4085	0.890333
  105.14 +4089	0.840333
  105.15 +4565	0.805667
  105.16 +4742	11.2947
  105.17 +4778	14.677
  105.18 +5395	2.54333
  105.19 +5587	3.559
  105.20 +5598	1.28433
  105.21 +5741	17.7933
  105.22 +6033	1.878
  105.23 +6357	3.084
  105.24 +6401	4.80367
  105.25 +6581	3.23567
  105.26 +6593	2.65867
  105.27 +6869	3.31867
  105.28 +7079	3.54667
  105.29 +7280	2.801
  105.30 +7882	9.438
  105.31 +8847	18.4517
  105.32 +9039	13.3743
  105.33 +9728	7.01267
   106.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   106.2 +++ b/randGraph/ind/vf2ppInd15_0.2.txt	Tue Nov 22 08:15:16 2016 +0100
   106.3 @@ -0,0 +1,30 @@
   106.4 +32	0.012
   106.5 +471	0.158667
   106.6 +1247	0.422667
   106.7 +2258	0.848
   106.8 +2333	0.870667
   106.9 +2339	0.860667
  106.10 +2344	0.877333
  106.11 +2642	1.05267
  106.12 +2756	0.966
  106.13 +3207	1.196
  106.14 +3593	1.27933
  106.15 +4212	1.534
  106.16 +5038	1.90733
  106.17 +5085	2.155
  106.18 +5543	2.518
  106.19 +5801	2.947
  106.20 +5861	3.33867
  106.21 +6042	2.218
  106.22 +6385	2.66867
  106.23 +6959	2.95133
  106.24 +7205	2.58767
  106.25 +8042	4.22967
  106.26 +8173	3.53733
  106.27 +9063	5.05867
  106.28 +9074	5.36933
  106.29 +9736	4.149
  106.30 +9770	6.145
  106.31 +9805	4.74167
  106.32 +9833	4.91367
  106.33 +9914	5.165
   107.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   107.2 +++ b/randGraph/ind/vf2ppInd15_0.3.txt	Tue Nov 22 08:15:16 2016 +0100
   107.3 @@ -0,0 +1,30 @@
   107.4 +262	0.135333
   107.5 +598	0.309333
   107.6 +694	0.366667
   107.7 +722	0.370333
   107.8 +752	0.379333
   107.9 +1116	0.585667
  107.10 +1224	0.645667
  107.11 +1293	0.698333
  107.12 +1314	0.681333
  107.13 +1836	0.994333
  107.14 +3127	1.80733
  107.15 +3213	1.82233
  107.16 +3390	2.109
  107.17 +3613	2.00933
  107.18 +4832	2.88533
  107.19 +5319	3.144
  107.20 +5330	3.16367
  107.21 +5379	3.43933
  107.22 +5394	3.18233
  107.23 +5456	3.38367
  107.24 +6354	4.65767
  107.25 +6579	3.926
  107.26 +6889	4.30833
  107.27 +7096	4.39633
  107.28 +8039	5.09067
  107.29 +8436	5.38967
  107.30 +8686	5.465
  107.31 +9377	6.039
  107.32 +9455	6.445
  107.33 +9608	6.16967
   108.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   108.2 +++ b/randGraph/ind/vf2ppInd15_0.4.txt	Tue Nov 22 08:15:16 2016 +0100
   108.3 @@ -0,0 +1,30 @@
   108.4 +30	0.0193333
   108.5 +315	0.226333
   108.6 +439	0.312333
   108.7 +717	0.533667
   108.8 +1550	1.21567
   108.9 +1859	1.512
  108.10 +1867	1.473
  108.11 +1868	1.52367
  108.12 +2687	2.25567
  108.13 +2734	2.37
  108.14 +3357	2.74433
  108.15 +3709	3.01867
  108.16 +5091	4.33667
  108.17 +5510	4.62033
  108.18 +5514	4.83333
  108.19 +5654	5.03467
  108.20 +5732	5.07067
  108.21 +6082	5.78367
  108.22 +6549	5.85133
  108.23 +6816	6.15333
  108.24 +6920	6.08967
  108.25 +7859	7.083
  108.26 +8363	7.626
  108.27 +8757	7.96433
  108.28 +8854	7.919
  108.29 +8868	8.09233
  108.30 +9036	8.47033
  108.31 +9515	8.78633
  108.32 +9686	8.83533
  108.33 +9782	9.45933
   109.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   109.2 +++ b/randGraph/ind/vf2ppInd15_0.5.txt	Tue Nov 22 08:15:16 2016 +0100
   109.3 @@ -0,0 +1,30 @@
   109.4 +313	0.319667
   109.5 +542	0.548667
   109.6 +623	0.64
   109.7 +1531	1.55567
   109.8 +1753	1.84767
   109.9 +1856	1.99567
  109.10 +1903	1.96733
  109.11 +2022	2.211
  109.12 +2064	2.209
  109.13 +3364	3.75433
  109.14 +3982	4.50333
  109.15 +4041	4.603
  109.16 +5037	5.99967
  109.17 +6089	7.01633
  109.18 +6443	7.47167
  109.19 +6638	7.72567
  109.20 +6892	8.05567
  109.21 +7005	8.47933
  109.22 +7133	8.693
  109.23 +7764	9.36267
  109.24 +7826	9.21667
  109.25 +7839	9.55367
  109.26 +7916	9.45433
  109.27 +8055	9.772
  109.28 +8075	9.816
  109.29 +8403	9.97067
  109.30 +8627	10.559
  109.31 +8701	10.5947
  109.32 +9207	11.37
  109.33 +9907	12.3923
   110.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   110.2 +++ b/randGraph/ind/vf2ppInd15_0.6.txt	Tue Nov 22 08:15:16 2016 +0100
   110.3 @@ -0,0 +1,30 @@
   110.4 +136	0.165667
   110.5 +1037	1.349
   110.6 +1104	1.43567
   110.7 +1198	1.58233
   110.8 +1204	1.641
   110.9 +1400	1.924
  110.10 +1533	2.02433
  110.11 +1669	2.29033
  110.12 +1723	2.36067
  110.13 +2230	3.12033
  110.14 +3701	5.424
  110.15 +4063	6.157
  110.16 +4258	6.25533
  110.17 +4476	6.64567
  110.18 +5205	7.83367
  110.19 +5304	8.06333
  110.20 +5718	8.58367
  110.21 +6123	9.443
  110.22 +6141	9.535
  110.23 +6192	9.48433
  110.24 +6711	10.6077
  110.25 +6973	11.155
  110.26 +7075	11.1143
  110.27 +7294	11.6163
  110.28 +7653	12.2893
  110.29 +7869	12.6847
  110.30 +7878	12.678
  110.31 +8668	13.8913
  110.32 +8726	14.3277
  110.33 +9523	15.6823
   111.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   111.2 +++ b/randGraph/ind/vf2ppInd15_0.7.txt	Tue Nov 22 08:15:16 2016 +0100
   111.3 @@ -0,0 +1,49 @@
   111.4 +115	0.172667
   111.5 +197	0.288333
   111.6 +364	0.552
   111.7 +392	0.621667
   111.8 +914	1.50733
   111.9 +950	1.57567
  111.10 +1556	2.613
  111.11 +1561	2.69567
  111.12 +1702	2.94833
  111.13 +1740	2.94633
  111.14 +1834	3.12
  111.15 +1982	3.45367
  111.16 +1998	3.46433
  111.17 +2023	3.472
  111.18 +2092	3.586
  111.19 +2187	3.82633
  111.20 +2297	4.02933
  111.21 +2314	4.08033
  111.22 +2399	4.28333
  111.23 +2450	4.43367
  111.24 +2534	4.54633
  111.25 +2570	4.59367
  111.26 +2666	4.739
  111.27 +2712	4.90267
  111.28 +2725	4.784
  111.29 +2729	4.82333
  111.30 +2730	4.883
  111.31 +2895	5.25267
  111.32 +2920	5.23633
  111.33 +2929	5.23967
  111.34 +2997	5.37767
  111.35 +3117	5.81833
  111.36 +3149	5.81033
  111.37 +3182	5.79967
  111.38 +3451	6.29767
  111.39 +3464	6.463
  111.40 +3537	6.45167
  111.41 +3564	6.591
  111.42 +3594	6.57067
  111.43 +3825	7.19667
  111.44 +3892	7.172
  111.45 +3972	7.33367
  111.46 +4198	8.09167
  111.47 +4243	7.99033
  111.48 +4281	8.07633
  111.49 +4327	8.302
  111.50 +4776	9.09833
  111.51 +4882	9.21733
  111.52 +4938	9.47633
   112.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   112.2 +++ b/randGraph/ind/vf2ppInd15_0.8.txt	Tue Nov 22 08:15:16 2016 +0100
   112.3 @@ -0,0 +1,30 @@
   112.4 +57	0.099
   112.5 +864	1.69167
   112.6 +1355	2.68633
   112.7 +1402	2.852
   112.8 +1580	3.21867
   112.9 +2161	4.597
  112.10 +2295	4.885
  112.11 +2368	5.01667
  112.12 +2585	5.51133
  112.13 +2720	5.82433
  112.14 +3126	6.803
  112.15 +3151	6.917
  112.16 +4218	9.72633
  112.17 +4886	11.0813
  112.18 +5022	11.658
  112.19 +5239	12.1167
  112.20 +5344	12.2433
  112.21 +5361	12.1497
  112.22 +5375	12.3153
  112.23 +5819	13.4813
  112.24 +5930	13.69
  112.25 +6273	14.7603
  112.26 +6477	15.2887
  112.27 +6947	16.3877
  112.28 +7598	18.3013
  112.29 +8269	19.8827
  112.30 +8736	21.7027
  112.31 +8868	21.4237
  112.32 +8972	21.9797
  112.33 +9725	23.7263
   113.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   113.2 +++ b/randGraph/ind/vf2ppInd15_0.95.txt	Tue Nov 22 08:15:16 2016 +0100
   113.3 @@ -0,0 +1,30 @@
   113.4 +28	0.058
   113.5 +322	0.729
   113.6 +449	1.04533
   113.7 +561	1.30933
   113.8 +848	2.12467
   113.9 +1519	4.12433
  113.10 +2125	5.89733
  113.11 +2211	6.30633
  113.12 +2218	6.33867
  113.13 +2232	6.37933
  113.14 +2533	7.33867
  113.15 +2622	7.69733
  113.16 +2892	8.50067
  113.17 +3128	9.12
  113.18 +3156	9.349
  113.19 +3379	9.994
  113.20 +3513	10.518
  113.21 +3807	11.3437
  113.22 +4061	12.1577
  113.23 +4750	14.4103
  113.24 +4767	14.4057
  113.25 +4768	14.575
  113.26 +5893	17.9827
  113.27 +6203	19.2467
  113.28 +8331	26.5803
  113.29 +8433	27.073
  113.30 +8547	27.4483
  113.31 +8935	28.6703
  113.32 +9613	31.179
  113.33 +9627	31.0557
   114.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   114.2 +++ b/randGraph/ind/vf2ppInd32_0.05.txt	Tue Nov 22 08:15:16 2016 +0100
   114.3 @@ -0,0 +1,30 @@
   114.4 +216	0.0256667
   114.5 +407	0.054
   114.6 +538	0.0753333
   114.7 +927	0.141667
   114.8 +1009	0.13
   114.9 +1277	0.182
  114.10 +1668	0.246333
  114.11 +2391	0.79
  114.12 +3229	0.588667
  114.13 +3754	1.11433
  114.14 +3953	1.711
  114.15 +4254	2.74767
  114.16 +4525	0.831
  114.17 +4780	2.55267
  114.18 +5281	3.972
  114.19 +5861	1.98633
  114.20 +6317	2.189
  114.21 +6434	2.517
  114.22 +6766	4.74233
  114.23 +6881	1.70067
  114.24 +7047	1.75867
  114.25 +7316	6.84733
  114.26 +7396	2.67267
  114.27 +8696	7.369
  114.28 +8897	64.127
  114.29 +9051	4.37267
  114.30 +9075	19.596
  114.31 +9377	7.534
  114.32 +9573	26.88
  114.33 +9687	30.3903
   115.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   115.2 +++ b/randGraph/ind/vf2ppInd32_0.1.txt	Tue Nov 22 08:15:16 2016 +0100
   115.3 @@ -0,0 +1,30 @@
   115.4 +344	0.0883333
   115.5 +1434	0.382333
   115.6 +2070	0.731333
   115.7 +2175	0.609667
   115.8 +2480	0.679
   115.9 +2685	0.820667
  115.10 +3150	1.18033
  115.11 +3611	1.29167
  115.12 +3814	1.39767
  115.13 +4085	1.19267
  115.14 +4089	1.387
  115.15 +4565	1.44533
  115.16 +4742	1.53067
  115.17 +4778	1.50533
  115.18 +5395	2.04567
  115.19 +5587	1.93833
  115.20 +5598	2.05633
  115.21 +5741	1.82233
  115.22 +6033	2.15367
  115.23 +6357	1.87467
  115.24 +6401	3.375
  115.25 +6581	2.27433
  115.26 +6593	2.21667
  115.27 +6869	2.19067
  115.28 +7079	2.73167
  115.29 +7280	3.381
  115.30 +7882	3.30433
  115.31 +8847	4.94833
  115.32 +9039	4.95233
  115.33 +9728	4.448
   116.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   116.2 +++ b/randGraph/ind/vf2ppInd32_0.3.txt	Tue Nov 22 08:15:16 2016 +0100
   116.3 @@ -0,0 +1,30 @@
   116.4 +262	0.222
   116.5 +598	0.523667
   116.6 +694	0.625333
   116.7 +722	0.641667
   116.8 +752	0.686667
   116.9 +1116	1.033
  116.10 +1224	1.14567
  116.11 +1293	1.21533
  116.12 +1314	1.231
  116.13 +1836	1.76667
  116.14 +3127	3.10133
  116.15 +3213	3.18767
  116.16 +3390	3.39567
  116.17 +3613	3.69567
  116.18 +4832	4.86967
  116.19 +5319	5.41767
  116.20 +5330	5.293
  116.21 +5379	5.45167
  116.22 +5394	5.40433
  116.23 +5456	5.504
  116.24 +6354	6.41133
  116.25 +6579	6.688
  116.26 +6889	7.098
  116.27 +7096	7.31133
  116.28 +8039	8.348
  116.29 +8436	8.902
  116.30 +8686	9.26267
  116.31 +9377	9.98467
  116.32 +9455	10.0533
  116.33 +9608	10.3483
   117.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   117.2 +++ b/randGraph/ind/vf2ppInd32_0.6.txt	Tue Nov 22 08:15:16 2016 +0100
   117.3 @@ -0,0 +1,30 @@
   117.4 +136	0.3
   117.5 +1037	2.623
   117.6 +1104	2.71433
   117.7 +1198	2.94267
   117.8 +1204	3.004
   117.9 +1400	3.534
  117.10 +1533	3.877
  117.11 +1669	4.27267
  117.12 +1723	4.46333
  117.13 +2230	5.88833
  117.14 +3701	10.3217
  117.15 +4063	12.1177
  117.16 +4258	11.9453
  117.17 +4476	12.628
  117.18 +5205	14.783
  117.19 +5304	15.1423
  117.20 +5718	16.596
  117.21 +6123	17.8053
  117.22 +6141	17.9073
  117.23 +6192	18.3197
  117.24 +6711	19.5373
  117.25 +6973	20.4103
  117.26 +7075	20.6033
  117.27 +7294	21.3557
  117.28 +7653	22.3623
  117.29 +7869	23.215
  117.30 +7878	23.1713
  117.31 +8668	25.939
  117.32 +8726	26.0967
  117.33 +9523	28.605
   118.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   118.2 +++ b/randGraph/ind/vf2ppInd32_0.8.txt	Tue Nov 22 08:15:16 2016 +0100
   118.3 @@ -0,0 +1,30 @@
   118.4 +248	0.872333
   118.5 +439	1.55767
   118.6 +443	1.63633
   118.7 +1328	5.37267
   118.8 +1471	6.00033
   118.9 +2396	10.006
  118.10 +2454	10.3023
  118.11 +2968	12.4067
  118.12 +2997	12.942
  118.13 +3149	13.509
  118.14 +3328	14.336
  118.15 +3472	14.9353
  118.16 +3850	16.56
  118.17 +4055	17.5867
  118.18 +5013	22.144
  118.19 +5059	23.2843
  118.20 +5663	25.5683
  118.21 +5728	26.1993
  118.22 +6077	28.2707
  118.23 +6448	29.18
  118.24 +6510	28.466
  118.25 +6532	29.3593
  118.26 +7140	31.576
  118.27 +7297	32.294
  118.28 +7470	33.6157
  118.29 +7628	33.767
  118.30 +8250	38.49
  118.31 +8333	39.233
  118.32 +8834	42.1883
  118.33 +9980	48.5733
   119.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   119.2 +++ b/randGraph/ind/vf2ppInd32_0.95.txt	Tue Nov 22 08:15:16 2016 +0100
   119.3 @@ -0,0 +1,30 @@
   119.4 +28	0.0763333
   119.5 +322	1.45067
   119.6 +449	2.122
   119.7 +561	2.68233
   119.8 +848	4.34533
   119.9 +1519	8.448
  119.10 +2125	11.5473
  119.11 +2211	12.187
  119.12 +2218	12.574
  119.13 +2232	12.2737
  119.14 +2533	14.052
  119.15 +2622	14.1437
  119.16 +2892	16.2433
  119.17 +3128	18.7247
  119.18 +3156	17.7963
  119.19 +3379	18.994
  119.20 +3513	20.174
  119.21 +3807	20.4843
  119.22 +4061	22.896
  119.23 +4750	25.737
  119.24 +4767	25.796
  119.25 +4768	26.983
  119.26 +5893	32.2643
  119.27 +6203	34.7197
  119.28 +8331	51.787
  119.29 +8433	53.5687
  119.30 +8547	54.17
  119.31 +8935	55.877
  119.32 +9613	59.2407
  119.33 +9627	59.24
   120.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   120.2 +++ b/randGraph/ind/vf2ppInd35_0.05.txt	Tue Nov 22 08:15:16 2016 +0100
   120.3 @@ -0,0 +1,47 @@
   120.4 +33	0.002
   120.5 +684	0.103333
   120.6 +1057	0.156333
   120.7 +1125	0.226333
   120.8 +1578	0.288
   120.9 +1860	0.441667
  120.10 +1867	0.375
  120.11 +1990	0.387
  120.12 +2036	0.582667
  120.13 +2595	0.420333
  120.14 +2607	0.611
  120.15 +2756	0.716667
  120.16 +3185	0.749333
  120.17 +3275	0.71
  120.18 +3362	1.171
  120.19 +3466	0.787667
  120.20 +3492	0.979667
  120.21 +3564	0.615667
  120.22 +3656	1.07733
  120.23 +3834	1.38467
  120.24 +4345	2.50567
  120.25 +4605	1.11367
  120.26 +4740	1.585
  120.27 +4921	1.08533
  120.28 +4941	1.28733
  120.29 +4993	1.187
  120.30 +5513	2.28133
  120.31 +5767	3.42267
  120.32 +6134	4.55433
  120.33 +6410	6.12933
  120.34 +6534	4.74933
  120.35 +6904	2.03367
  120.36 +7010	11.2137
  120.37 +7067	3.02833
  120.38 +7231	2.602
  120.39 +7314	5.80833
  120.40 +7525	4.636
  120.41 +7538	5.51833
  120.42 +7660	3.01067
  120.43 +8422	8.947
  120.44 +8696	19.85
  120.45 +8885	13.444
  120.46 +8916	8.696
  120.47 +8919	4.75467
  120.48 +9337	8.49733
  120.49 +9878	10.3503
  120.50 +9999	12.4133
   121.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   121.2 +++ b/randGraph/ind/vf2ppInd35_0.1.txt	Tue Nov 22 08:15:16 2016 +0100
   121.3 @@ -0,0 +1,50 @@
   121.4 +302	0.0766667
   121.5 +450	0.119
   121.6 +697	0.204
   121.7 +744	0.202333
   121.8 +805	0.222333
   121.9 +938	0.259667
  121.10 +963	0.287667
  121.11 +1043	0.302
  121.12 +1240	0.402667
  121.13 +1797	0.548
  121.14 +2018	0.637667
  121.15 +2124	0.641
  121.16 +2435	0.864333
  121.17 +2810	0.999333
  121.18 +3368	1.06533
  121.19 +3401	1.177
  121.20 +3531	1.17
  121.21 +3674	1.36033
  121.22 +3734	1.14833
  121.23 +4359	1.41933
  121.24 +4403	1.459
  121.25 +4406	1.82333
  121.26 +4466	1.49833
  121.27 +4579	1.647
  121.28 +4685	1.49167
  121.29 +4940	1.68467
  121.30 +5007	1.70733
  121.31 +5312	1.733
  121.32 +5471	1.767
  121.33 +5564	2.71533
  121.34 +5962	2.27367
  121.35 +6114	2.51267
  121.36 +6677	2.802
  121.37 +7019	2.60933
  121.38 +7128	2.97933
  121.39 +7468	2.61133
  121.40 +7488	2.498
  121.41 +7636	3.679
  121.42 +7668	4.28667
  121.43 +7823	2.94333
  121.44 +8143	4.04233
  121.45 +8156	3.09033
  121.46 +8333	3.767
  121.47 +8572	3.66367
  121.48 +8961	5.04967
  121.49 +9009	3.94867
  121.50 +9443	4.829
  121.51 +9784	4.55167
  121.52 +9868	3.76567
  121.53 +9959	3.98567
   122.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   122.2 +++ b/randGraph/ind/vf2ppInd35_0.3.txt	Tue Nov 22 08:15:16 2016 +0100
   122.3 @@ -0,0 +1,50 @@
   122.4 +326	0.305333
   122.5 +399	0.372333
   122.6 +476	0.450333
   122.7 +1069	1.09433
   122.8 +1389	1.456
   122.9 +1415	1.48867
  122.10 +1654	1.74733
  122.11 +1909	1.978
  122.12 +1961	2.06433
  122.13 +2638	2.839
  122.14 +3005	3.26433
  122.15 +3045	3.39367
  122.16 +3144	3.45867
  122.17 +3229	3.54833
  122.18 +3275	3.603
  122.19 +3803	4.04133
  122.20 +4459	4.956
  122.21 +4816	5.32667
  122.22 +4988	5.50933
  122.23 +5097	5.647
  122.24 +5424	6.02467
  122.25 +5465	6.09067
  122.26 +5634	6.33367
  122.27 +5645	6.24233
  122.28 +6022	6.81033
  122.29 +6094	6.83167
  122.30 +6159	6.803
  122.31 +6291	7.09933
  122.32 +6361	7.144
  122.33 +6638	7.70633
  122.34 +6677	7.56567
  122.35 +6838	7.53833
  122.36 +7043	8.01667
  122.37 +7531	8.29867
  122.38 +7566	8.32933
  122.39 +7623	8.47833
  122.40 +7647	8.54567
  122.41 +7822	8.67933
  122.42 +7994	8.86367
  122.43 +8003	8.98133
  122.44 +8475	10.0393
  122.45 +8996	10.6107
  122.46 +9118	10.5393
  122.47 +9256	11.244
  122.48 +9702	11.1997
  122.49 +9750	11.3573
  122.50 +9753	11.3957
  122.51 +9787	11.4
  122.52 +9848	11.467
  122.53 +9849	12.043
   123.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   123.2 +++ b/randGraph/ind/vf2ppInd35_0.6.txt	Tue Nov 22 08:15:16 2016 +0100
   123.3 @@ -0,0 +1,50 @@
   123.4 +379	0.943333
   123.5 +431	1.11667
   123.6 +665	1.804
   123.7 +718	1.83133
   123.8 +826	2.151
   123.9 +1251	3.39333
  123.10 +1279	3.49767
  123.11 +1443	4.16333
  123.12 +1500	4.27933
  123.13 +2193	6.26067
  123.14 +2231	6.265
  123.15 +2280	6.45067
  123.16 +2632	7.407
  123.17 +2687	7.696
  123.18 +2907	8.28067
  123.19 +3053	8.77467
  123.20 +3091	8.99
  123.21 +3437	10.057
  123.22 +3587	10.6527
  123.23 +3976	11.5893
  123.24 +4702	14.2217
  123.25 +4751	14.1807
  123.26 +5349	16.8533
  123.27 +5350	16.7427
  123.28 +5353	16.4263
  123.29 +5722	17.5457
  123.30 +5764	17.609
  123.31 +5844	17.6013
  123.32 +5946	18.1777
  123.33 +5969	18.356
  123.34 +5993	18.331
  123.35 +6013	18.586
  123.36 +6323	19.724
  123.37 +6883	21.5973
  123.38 +6917	21.8227
  123.39 +7218	22.7117
  123.40 +7383	23.3807
  123.41 +7663	24.1823
  123.42 +8038	26.0197
  123.43 +8119	25.9057
  123.44 +8133	25.7447
  123.45 +8165	25.8963
  123.46 +8204	26.8807
  123.47 +8694	27.3007
  123.48 +8805	29.443
  123.49 +9262	29.2483
  123.50 +9334	30.2993
  123.51 +9569	30.4333
  123.52 +9811	31.097
  123.53 +9876	31.6503
   124.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   124.2 +++ b/randGraph/ind/vf2ppInd35_0.8.txt	Tue Nov 22 08:15:16 2016 +0100
   124.3 @@ -0,0 +1,50 @@
   124.4 +22	0.0393333
   124.5 +155	0.571667
   124.6 +176	0.630333
   124.7 +911	3.962
   124.8 +1065	4.58933
   124.9 +1107	4.76133
  124.10 +1526	7.139
  124.11 +1623	7.289
  124.12 +1782	7.93
  124.13 +1863	8.31633
  124.14 +1911	8.60933
  124.15 +2165	10.078
  124.16 +2192	10.0547
  124.17 +2217	10.0457
  124.18 +2247	9.949
  124.19 +3050	14.1343
  124.20 +3167	14.7493
  124.21 +3398	16.012
  124.22 +3627	16.2417
  124.23 +4092	19.0117
  124.24 +4240	19.2673
  124.25 +4346	20.274
  124.26 +4615	21.8037
  124.27 +4673	23.27
  124.28 +4708	22.9527
  124.29 +4739	21.8833
  124.30 +4818	23.3217
  124.31 +5058	23.948
  124.32 +5222	24.4
  124.33 +5414	25.2407
  124.34 +5868	27.4257
  124.35 +5946	30.0323
  124.36 +6061	28.5753
  124.37 +6263	30.288
  124.38 +6611	32.98
  124.39 +6699	32.8473
  124.40 +6799	33.324
  124.41 +6915	33.991
  124.42 +7100	34.5173
  124.43 +7136	35.7403
  124.44 +7218	36.1373
  124.45 +7369	36.3943
  124.46 +7736	39.464
  124.47 +8219	43.719
  124.48 +8377	43.019
  124.49 +8482	43.3823
  124.50 +8632	43.822
  124.51 +8886	47.0287
  124.52 +9351	49.2603
  124.53 +9771	52.7797
   125.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   125.2 +++ b/randGraph/ind/vf2ppInd35_0.95.txt	Tue Nov 22 08:15:16 2016 +0100
   125.3 @@ -0,0 +1,49 @@
   125.4 +20	0.0413333
   125.5 +550	2.86733
   125.6 +628	3.361
   125.7 +660	3.513
   125.8 +1192	6.79433
   125.9 +1663	9.78133
  125.10 +1749	10.8153
  125.11 +1768	10.407
  125.12 +2082	12.0513
  125.13 +2355	14.6867
  125.14 +2375	13.79
  125.15 +2617	15.323
  125.16 +2946	17.9003
  125.17 +3499	21.046
  125.18 +3567	21.276
  125.19 +3774	25.3113
  125.20 +3923	23.951
  125.21 +4002	24.817
  125.22 +4189	25.452
  125.23 +4205	26.0877
  125.24 +4214	26.499
  125.25 +4414	26.8313
  125.26 +4430	26.8737
  125.27 +4481	27.4707
  125.28 +4500	28.364
  125.29 +4706	28.8917
  125.30 +4861	29.77
  125.31 +5162	31.4247
  125.32 +5650	35.2547
  125.33 +5724	35.5233
  125.34 +5795	35.4867
  125.35 +5938	37.4263
  125.36 +5944	37.0227
  125.37 +6006	38.4617
  125.38 +6057	42.5057
  125.39 +6462	41.0057
  125.40 +6536	41.8393
  125.41 +6668	43.6183
  125.42 +6996	46.7797
  125.43 +7594	49.0137
  125.44 +7936	52.2893
  125.45 +8716	56.329
  125.46 +8871	55.0203
  125.47 +9032	58.0967
  125.48 +9142	58.6687
  125.49 +9164	66.3373
  125.50 +9435	58.8493
  125.51 +9465	67.1867
  125.52 +9792	69.378
   126.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   126.2 +++ b/randGraph/ind/vf2ppInd5_0.05.txt	Tue Nov 22 08:15:16 2016 +0100
   126.3 @@ -0,0 +1,49 @@
   126.4 +354	0.0166667
   126.5 +446	0.022
   126.6 +631	0.033
   126.7 +668	0.033
   126.8 +842	0.0453333
   126.9 +1296	0.065
  126.10 +1327	0.0686667
  126.11 +1495	0.073
  126.12 +1713	0.089
  126.13 +2027	0.103
  126.14 +2106	0.111667
  126.15 +2901	0.144
  126.16 +2967	0.152333
  126.17 +3169	0.180333
  126.18 +3279	0.189
  126.19 +3320	0.176667
  126.20 +3510	0.183
  126.21 +4337	0.236333
  126.22 +4535	0.235333
  126.23 +4841	0.256333
  126.24 +5020	0.272
  126.25 +5111	0.274333
  126.26 +5163	0.357333
  126.27 +5359	0.331333
  126.28 +5542	0.288333
  126.29 +5547	0.279333
  126.30 +5562	0.296667
  126.31 +5631	0.298
  126.32 +5877	0.299333
  126.33 +6101	0.361333
  126.34 +6295	0.339667
  126.35 +6584	0.346667
  126.36 +6594	0.573333
  126.37 +6788	0.375333
  126.38 +6849	0.406
  126.39 +7173	0.384667
  126.40 +7279	0.385333
  126.41 +7361	0.722
  126.42 +7384	0.412667
  126.43 +7461	0.425
  126.44 +7467	0.461
  126.45 +8091	0.476667
  126.46 +8451	0.506
  126.47 +8827	0.451333
  126.48 +9031	0.574
  126.49 +9134	1.27267
  126.50 +9639	0.583
  126.51 +9720	0.682
  126.52 +9943	0.648333
   127.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   127.2 +++ b/randGraph/ind/vf2ppInd5_0.1.txt	Tue Nov 22 08:15:16 2016 +0100
   127.3 @@ -0,0 +1,48 @@
   127.4 +70	0.006
   127.5 +377	0.035
   127.6 +390	0.038
   127.7 +788	0.0723333
   127.8 +1086	0.102333
   127.9 +1922	0.177
  127.10 +2057	0.193
  127.11 +2071	0.196
  127.12 +2169	0.227333
  127.13 +2406	0.238667
  127.14 +2958	0.366333
  127.15 +3323	0.347333
  127.16 +3631	0.4
  127.17 +4224	0.624333
  127.18 +4380	0.49
  127.19 +4427	0.642
  127.20 +4663	0.521667
  127.21 +4942	0.742333
  127.22 +5118	0.578
  127.23 +5183	0.657667
  127.24 +5204	0.573
  127.25 +5368	0.611667
  127.26 +5704	0.642
  127.27 +5826	0.613667
  127.28 +5859	0.588
  127.29 +5925	0.634667
  127.30 +5948	0.676667
  127.31 +5961	0.786
  127.32 +6052	0.672333
  127.33 +6472	0.674667
  127.34 +6871	0.838667
  127.35 +7015	0.833
  127.36 +7039	1.065
  127.37 +7221	1.371
  127.38 +7238	15.657
  127.39 +7776	1.20033
  127.40 +7806	0.818
  127.41 +8478	2.17133
  127.42 +8679	3.082
  127.43 +8966	7.78167
  127.44 +9251	1.44833
  127.45 +9336	15.544
  127.46 +9499	1.076
  127.47 +9583	1.40233
  127.48 +9585	58.2783
  127.49 +9649	1.74167
  127.50 +9816	4.50733
  127.51 +9932	2.14333
   128.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   128.2 +++ b/randGraph/ind/vf2ppInd5_0.3.txt	Tue Nov 22 08:15:16 2016 +0100
   128.3 @@ -0,0 +1,48 @@
   128.4 +326	0.0933333
   128.5 +399	0.118333
   128.6 +476	0.136
   128.7 +1069	0.345667
   128.8 +1389	0.458667
   128.9 +1415	0.462333
  128.10 +1654	0.489
  128.11 +1909	0.566333
  128.12 +1961	0.579
  128.13 +2638	0.995333
  128.14 +3005	0.898667
  128.15 +3045	1.058
  128.16 +3144	1.033
  128.17 +3229	1.057
  128.18 +3275	1.29667
  128.19 +3803	1.158
  128.20 +4459	1.47133
  128.21 +4816	1.68333
  128.22 +4988	2.487
  128.23 +5097	2.03067
  128.24 +5424	2.01667
  128.25 +5465	2.03633
  128.26 +5634	1.9
  128.27 +5645	2.21233
  128.28 +6022	2.241
  128.29 +6094	3.47567
  128.30 +6159	2.819
  128.31 +6291	2.505
  128.32 +6361	6.54433
  128.33 +6638	11.287
  128.34 +6677	3.48567
  128.35 +6838	3.951
  128.36 +7043	3.713
  128.37 +7531	2.717
  128.38 +7566	2.86233
  128.39 +7623	4.40867
  128.40 +7647	4.656
  128.41 +7822	4.36233
  128.42 +7994	3.64
  128.43 +8003	5.27433
  128.44 +8475	6.34667
  128.45 +8996	6.25967
  128.46 +9118	4.21533
  128.47 +9750	23.6907
  128.48 +9753	5.349
  128.49 +9787	5.91533
  128.50 +9848	6.192
  128.51 +9849	10.102
   129.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   129.2 +++ b/randGraph/ind/vf2ppInd5_0.6.txt	Tue Nov 22 08:15:16 2016 +0100
   129.3 @@ -0,0 +1,50 @@
   129.4 +379	0.226
   129.5 +431	0.26
   129.6 +665	0.398
   129.7 +718	0.424667
   129.8 +826	0.503333
   129.9 +1251	0.784333
  129.10 +1279	0.785667
  129.11 +1443	0.904
  129.12 +1500	0.946667
  129.13 +2193	1.41733
  129.14 +2231	1.445
  129.15 +2280	1.49333
  129.16 +2632	1.776
  129.17 +2687	1.836
  129.18 +2907	1.90867
  129.19 +3053	2.04767
  129.20 +3091	2.11767
  129.21 +3437	2.47367
  129.22 +3587	2.62867
  129.23 +3976	2.693
  129.24 +4702	3.98433
  129.25 +4751	3.34633
  129.26 +5349	4.24767
  129.27 +5350	4.414
  129.28 +5353	3.749
  129.29 +5722	4.31667
  129.30 +5764	4.34967
  129.31 +5844	4.79067
  129.32 +5946	4.254
  129.33 +5969	4.63667
  129.34 +5993	4.403
  129.35 +6013	4.73267
  129.36 +6323	4.629
  129.37 +6883	5.247
  129.38 +6917	6.433
  129.39 +7218	5.329
  129.40 +7383	5.45233
  129.41 +7663	5.998
  129.42 +8038	6.07867
  129.43 +8119	5.91267
  129.44 +8133	6.55067
  129.45 +8165	6.58833
  129.46 +8204	6.14433
  129.47 +8694	6.402
  129.48 +8805	7.31933
  129.49 +9262	7.337
  129.50 +9334	7.96067
  129.51 +9569	8.64567
  129.52 +9811	7.92667
  129.53 +9876	9.43567
   130.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   130.2 +++ b/randGraph/ind/vf2ppInd5_0.8.txt	Tue Nov 22 08:15:16 2016 +0100
   130.3 @@ -0,0 +1,50 @@
   130.4 +22	0.016
   130.5 +155	0.129667
   130.6 +176	0.139667
   130.7 +911	0.797333
   130.8 +1065	0.919
   130.9 +1107	0.971333
  130.10 +1526	1.38433
  130.11 +1623	1.472
  130.12 +1782	1.65067
  130.13 +1863	1.70633
  130.14 +1911	1.76667
  130.15 +2165	2.38267
  130.16 +2192	2.04267
  130.17 +2217	2.12933
  130.18 +2247	2.09467
  130.19 +3050	2.965
  130.20 +3167	3.10467
  130.21 +3398	3.517
  130.22 +3627	3.529
  130.23 +4092	4.08667
  130.24 +4240	4.17667
  130.25 +4346	4.381
  130.26 +4615	4.61533
  130.27 +4673	4.68533
  130.28 +4708	4.75833
  130.29 +4739	4.811
  130.30 +4818	4.84
  130.31 +5058	5.27267
  130.32 +5222	5.36067
  130.33 +5414	5.62467
  130.34 +5868	6.06767
  130.35 +5946	6.277
  130.36 +6061	6.354
  130.37 +6263	6.612
  130.38 +6611	7.035
  130.39 +6699	7.41967
  130.40 +6799	7.291
  130.41 +6915	7.52767
  130.42 +7100	8.37267
  130.43 +7136	7.69
  130.44 +7218	7.85467
  130.45 +7369	8.376
  130.46 +7736	8.47367
  130.47 +8219	8.76167
  130.48 +8377	8.928
  130.49 +8482	9.275
  130.50 +8632	9.286
  130.51 +8886	9.56033
  130.52 +9351	10.1563
  130.53 +9771	10.635
   131.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   131.2 +++ b/randGraph/ind/vf2ppInd5_0.95.txt	Tue Nov 22 08:15:16 2016 +0100
   131.3 @@ -0,0 +1,49 @@
   131.4 +20	0.017
   131.5 +550	0.581333
   131.6 +628	0.666667
   131.7 +660	0.68
   131.8 +1192	1.278
   131.9 +1663	1.866
  131.10 +1749	1.997
  131.11 +1768	2.01533
  131.12 +2082	2.39367
  131.13 +2355	2.81433
  131.14 +2375	2.87133
  131.15 +2617	3.139
  131.16 +2946	3.63033
  131.17 +3499	4.28467
  131.18 +3567	4.39733
  131.19 +3774	4.69433
  131.20 +3923	4.88467
  131.21 +4002	4.96033
  131.22 +4189	5.24467
  131.23 +4205	5.207
  131.24 +4214	5.22567
  131.25 +4414	5.62767
  131.26 +4430	5.663
  131.27 +4481	5.681
  131.28 +4500	5.72767
  131.29 +4706	6.06867
  131.30 +4861	6.368
  131.31 +5162	6.70533
  131.32 +5650	7.55067
  131.33 +5724	7.42167
  131.34 +5795	7.68333
  131.35 +5938	7.843
  131.36 +5944	7.83067
  131.37 +6006	7.95533
  131.38 +6057	8.11267
  131.39 +6462	8.7
  131.40 +6536	8.81
  131.41 +6668	9.71067
  131.42 +6996	9.32
  131.43 +7594	10.5173
  131.44 +7936	10.8687
  131.45 +8716	11.93
  131.46 +8871	12.0603
  131.47 +9032	12.4133
  131.48 +9142	12.7773
  131.49 +9164	12.6763
  131.50 +9435	12.9623
  131.51 +9465	13.0667
  131.52 +9792	13.6357
   132.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   132.2 +++ b/randGraph/ind/vf2ppInd7_0.05.txt	Tue Nov 22 08:15:16 2016 +0100
   132.3 @@ -0,0 +1,30 @@
   132.4 +78	0.00366667
   132.5 +104	0.00533333
   132.6 +132	0.00633333
   132.7 +142	0.00866667
   132.8 +173	0.00833333
   132.9 +196	0.0103333
  132.10 +218	0.0123333
  132.11 +276	0.014
  132.12 +293	0.0156667
  132.13 +296	0.0143333
  132.14 +366	0.0203333
  132.15 +423	0.0233333
  132.16 +458	0.0263333
  132.17 +460	0.0263333
  132.18 +486	0.0263333
  132.19 +561	0.033
  132.20 +575	0.032
  132.21 +641	0.039
  132.22 +792	0.0436667
  132.23 +870	0.049
  132.24 +922	0.0526667
  132.25 +992	0.0726667
  132.26 +1114	0.0606667
  132.27 +1166	0.0656667
  132.28 +1202	0.0696667
  132.29 +1608	0.0873333
  132.30 +1737	0.107333
  132.31 +2022	0.123
  132.32 +2837	0.154
  132.33 +3271	0.196333
   133.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   133.2 +++ b/randGraph/ind/vf2ppInd7_0.1.txt	Tue Nov 22 08:15:16 2016 +0100
   133.3 @@ -0,0 +1,30 @@
   133.4 +47	0.00366667
   133.5 +85	0.008
   133.6 +150	0.0143333
   133.7 +192	0.02
   133.8 +200	0.02
   133.9 +206	0.02
  133.10 +273	0.0296667
  133.11 +302	0.032
  133.12 +387	0.0383333
  133.13 +394	0.0386667
  133.14 +536	0.0566667
  133.15 +790	0.0783333
  133.16 +816	0.0896667
  133.17 +851	0.0913333
  133.18 +925	0.0976667
  133.19 +1085	0.140333
  133.20 +1107	0.114
  133.21 +1135	0.119333
  133.22 +1460	0.164333
  133.23 +1488	0.178333
  133.24 +1954	0.235667
  133.25 +2054	0.225
  133.26 +2170	0.392
  133.27 +2190	0.242333
  133.28 +2253	1.291
  133.29 +2257	0.244
  133.30 +2311	0.34
  133.31 +2390	0.256333
  133.32 +2463	0.263
  133.33 +3366	0.619
   134.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   134.2 +++ b/randGraph/ind/vf2ppInd7_0.3.txt	Tue Nov 22 08:15:16 2016 +0100
   134.3 @@ -0,0 +1,28 @@
   134.4 +20	0.00566667
   134.5 +47	0.0143333
   134.6 +65	0.02
   134.7 +82	0.0273333
   134.8 +85	0.0256667
   134.9 +101	0.0316667
  134.10 +141	0.0433333
  134.11 +213	0.069
  134.12 +228	0.071
  134.13 +272	0.09
  134.14 +277	0.0963333
  134.15 +355	0.124
  134.16 +491	0.160667
  134.17 +587	0.187
  134.18 +654	0.223
  134.19 +698	0.231333
  134.20 +716	0.241
  134.21 +763	0.272
  134.22 +851	0.289333
  134.23 +1032	0.357
  134.24 +1095	0.358333
  134.25 +1603	0.537333
  134.26 +1969	0.708667
  134.27 +2176	0.757333
  134.28 +2412	1.07333
  134.29 +2587	1.00167
  134.30 +2958	1.048
  134.31 +4266	1.70767
   135.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   135.2 +++ b/randGraph/ind/vf2ppInd7_0.6.txt	Tue Nov 22 08:15:16 2016 +0100
   135.3 @@ -0,0 +1,29 @@
   135.4 +20	0.015
   135.5 +25	0.0166667
   135.6 +43	0.033
   135.7 +56	0.0423333
   135.8 +227	0.162667
   135.9 +397	0.290333
  135.10 +448	0.333333
  135.11 +474	0.351
  135.12 +487	0.353667
  135.13 +509	0.369667
  135.14 +630	0.456333
  135.15 +727	0.545
  135.16 +732	0.553333
  135.17 +777	0.593333
  135.18 +826	0.62
  135.19 +899	0.666333
  135.20 +1034	0.788
  135.21 +1078	0.797667
  135.22 +1107	0.845333
  135.23 +1146	0.889333
  135.24 +1282	1.01867
  135.25 +1393	1.06933
  135.26 +1410	1.108
  135.27 +1484	1.154
  135.28 +1600	1.25333
  135.29 +2053	1.76267
  135.30 +2076	1.62967
  135.31 +2201	1.75733
  135.32 +2813	2.30467
   136.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   136.2 +++ b/randGraph/ind/vf2ppInd7_0.8.txt	Tue Nov 22 08:15:16 2016 +0100
   136.3 @@ -0,0 +1,30 @@
   136.4 +37	0.0366667
   136.5 +70	0.0686667
   136.6 +157	0.164333
   136.7 +199	0.208667
   136.8 +271	0.276667
   136.9 +376	0.403
  136.10 +379	0.399667
  136.11 +380	0.404
  136.12 +522	0.564333
  136.13 +554	0.597667
  136.14 +595	0.658667
  136.15 +634	0.67
  136.16 +718	0.777
  136.17 +721	0.789333
  136.18 +730	0.787
  136.19 +928	1.02833
  136.20 +1046	1.168
  136.21 +1088	1.19933
  136.22 +1156	1.28133
  136.23 +1357	1.53
  136.24 +1443	1.62433
  136.25 +1564	1.788
  136.26 +1579	1.79267
  136.27 +1780	2.067
  136.28 +1860	2.16867
  136.29 +1876	2.22433
  136.30 +2079	2.429
  136.31 +2866	3.45133
  136.32 +3318	4.071
  136.33 +4068	5.20433
   137.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   137.2 +++ b/randGraph/ind/vf2ppInd7_0.95.txt	Tue Nov 22 08:15:16 2016 +0100
   137.3 @@ -0,0 +1,28 @@
   137.4 +20	0.029
   137.5 +59	0.0793333
   137.6 +80	0.106
   137.7 +108	0.137667
   137.8 +166	0.235
   137.9 +176	0.238667
  137.10 +222	0.303333
  137.11 +444	0.61
  137.12 +624	0.854333
  137.13 +631	0.857
  137.14 +669	0.906333
  137.15 +757	1.02633
  137.16 +876	1.198
  137.17 +891	1.20467
  137.18 +1124	1.565
  137.19 +1193	1.66233
  137.20 +1217	1.75233
  137.21 +1345	1.89033
  137.22 +1449	2.063
  137.23 +1603	2.35167
  137.24 +1655	2.424
  137.25 +2079	3.209
  137.26 +2129	3.17833
  137.27 +2567	3.89
  137.28 +2716	4.233
  137.29 +3103	4.88267
  137.30 +3657	5.85833
  137.31 +4945	8.292
   138.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   138.2 +++ b/randGraph/iso/vf2pIso.txt	Tue Nov 22 08:15:16 2016 +0100
   138.3 @@ -0,0 +1,149 @@
   138.4 +127	0.3269
   138.5 +162	0.432
   138.6 +240	0.7383
   138.7 +376	1.2215
   138.8 +425	1.4418
   138.9 +491	1.7892
  138.10 +653	2.6752
  138.11 +690	2.954
  138.12 +896	4.3193
  138.13 +985	4.9454
  138.14 +1003	5.0853
  138.15 +1030	5.3009
  138.16 +1132	6.187
  138.17 +1328	7.918
  138.18 +1942	14.7931
  138.19 +2226	19.1137
  138.20 +2472	22.4367
  138.21 +2804	28.1592
  138.22 +2818	28.1566
  138.23 +2907	30.4856
  138.24 +2930	30.6408
  138.25 +3076	34.0425
  138.26 +3200	35.2525
  138.27 +3364	39.1791
  138.28 +3467	41.12
  138.29 +3544	42.2586
  138.30 +3613	44.5656
  138.31 +3704	45.6906
  138.32 +3946	51.1882
  138.33 +4023	53.1333
  138.34 +4076	55.1514
  138.35 +4145	56.5863
  138.36 +4183	57.0518
  138.37 +4426	64.6284
  138.38 +4644	71.1045
  138.39 +4767	73.4162
  138.40 +5112	81.686
  138.41 +5204	84.8276
  138.42 +5243	88.8607
  138.43 +5263	87.1636
  138.44 +5384	90.1785
  138.45 +5408	93.2033
  138.46 +5490	93.4534
  138.47 +5653	101.436
  138.48 +5783	103.567
  138.49 +5861	108.921
  138.50 +5873	105.73
  138.51 +6014	110.53
  138.52 +6135	118.937
  138.53 +6340	121.431
  138.54 +6378	122.979
  138.55 +6443	125.289
  138.56 +6530	132.548
  138.57 +6822	139.731
  138.58 +7086	151.391
  138.59 +7180	152.987
  138.60 +7464	165.421
  138.61 +7504	171.694
  138.62 +7509	170.031
  138.63 +8175	201.68
  138.64 +8291	201.49
  138.65 +8478	209.186
  138.66 +8480	209.196
  138.67 +8622	220.353
  138.68 +8626	223.71
  138.69 +8904	230.857
  138.70 +8936	232.141
  138.71 +9189	244.022
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  138.73 +9249	255.463
  138.74 +9558	263.282
  138.75 +9630	271.048
  138.76 +10031	289.299
  138.77 +10493	324.825
  138.78 +10529	316.988
  138.79 +10873	347.361
  138.80 +10895	338.602
  138.81 +10966	342.686
  138.82 +10977	343.294
  138.83 +10994	354.913
  138.84 +11060	349.165
  138.85 +11204	356.526
  138.86 +11286	372.999
  138.87 +11314	363.811
  138.88 +11378	373.179
  138.89 +11553	378.583
  138.90 +11582	387.468
  138.91 +11723	390.035
  138.92 +11841	396.816
  138.93 +11979	405.154
  138.94 +11998	407.449
  138.95 +12223	421.647
  138.96 +12233	422.152
  138.97 +12509	451.354
  138.98 +12518	442.427
  138.99 +13063	479.332
 138.100 +13109	483.504
 138.101 +13223	501.017
 138.102 +13294	512.705
 138.103 +13328	499.509
 138.104 +13434	517.922
 138.105 +13537	527.302
 138.106 +13786	543.749
 138.107 +13865	539.42
 138.108 +14002	548.837
 138.109 +14031	552.555
 138.110 +14082	556.61
 138.111 +14163	563.011
 138.112 +14247	567.519
 138.113 +14629	597.366
 138.114 +14904	623.21
 138.115 +14981	631.806
 138.116 +15258	653.052
 138.117 +15437	665.189
 138.118 +15509	686.911
 138.119 +15886	703.382
 138.120 +15906	703.776
 138.121 +16099	732.679
 138.122 +16328	743.431
 138.123 +16346	743.708
 138.124 +16791	807.157
 138.125 +16801	789.883
 138.126 +16825	792.622
 138.127 +16841	791.928
 138.128 +16933	818.123
 138.129 +16999	806.333
 138.130 +17001	815.739
 138.131 +17047	813.86
 138.132 +17121	817.818
 138.133 +17292	833.62
 138.134 +17525	856.627
 138.135 +17669	867.454
 138.136 +17773	880.85
 138.137 +17911	911.295
 138.138 +18099	911.129
 138.139 +18160	931.889
 138.140 +18263	926.688
 138.141 +18347	935.971
 138.142 +18443	957.162
 138.143 +18462	945.711
 138.144 +18567	955.508
 138.145 +18675	969.268
 138.146 +18882	995.408
 138.147 +18946	995.628
 138.148 +19131	1013.69
 138.149 +19695	1105.03
 138.150 +19723	1082.63
 138.151 +19952	1102.51
 138.152 +19978	1105.65
   139.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   139.2 +++ b/randGraph/iso/vf2pIso100_1.txt	Tue Nov 22 08:15:16 2016 +0100
   139.3 @@ -0,0 +1,150 @@
   139.4 +91	1.08833
   139.5 +338	6.11567
   139.6 +394	7.28833
   139.7 +536	10.3657
   139.8 +697	14.1443
   139.9 +724	14.75
  139.10 +956	20.388
  139.11 +1167	26.529
  139.12 +1456	34.0203
  139.13 +1504	34.231
  139.14 +1829	45.5837
  139.15 +2052	50.555
  139.16 +2077	53.5503
  139.17 +2160	56.4827
  139.18 +2384	63.9643
  139.19 +2405	65.0017
  139.20 +2493	67.616
  139.21 +2741	72.3953
  139.22 +2743	74.0677
  139.23 +2835	77.836
  139.24 +2959	84.2507
  139.25 +3014	84.1323
  139.26 +3083	90.649
  139.27 +3097	87.8843
  139.28 +3311	95.6327
  139.29 +3527	106.306
  139.30 +3666	108.645
  139.31 +3693	112.026
  139.32 +3785	118.908
  139.33 +3794	113.779
  139.34 +3946	123.122
  139.35 +4134	136.734
  139.36 +4159	132.431
  139.37 +4298	142.579
  139.38 +4304	142.895
  139.39 +4334	142.756
  139.40 +4532	149.643
  139.41 +4690	159.618
  139.42 +4837	173.229
  139.43 +4898	171.443
  139.44 +5151	186.274
  139.45 +5483	216.96
  139.46 +5597	212.2
  139.47 +5642	214.346
  139.48 +6236	257.877
  139.49 +6311	255.037
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  139.51 +6663	285.598
  139.52 +7273	320.402
  139.53 +7317	332.526
  139.54 +7370	335.625
  139.55 +7898	370.01
  139.56 +7911	367.479
  139.57 +8097	386.562
  139.58 +8123	390.304
  139.59 +8412	408.048
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  139.61 +8710	431.012
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  139.63 +8777	437.838
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  139.66 +8914	450.318
  139.67 +8937	463.288
  139.68 +8975	454.932
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  139.70 +9008	461.497
  139.71 +9023	455.363
  139.72 +9194	469.333
  139.73 +9315	478.856
  139.74 +9384	484.936
  139.75 +9581	506.079
  139.76 +9906	538.191
  139.77 +10061	550.113
  139.78 +10234	565.127
  139.79 +10436	588.116
  139.80 +10568	608.76
  139.81 +10570	597.874
  139.82 +10830	622.351
  139.83 +10867	624.599
  139.84 +10934	629.65
  139.85 +10951	634.455
  139.86 +11003	636.137
  139.87 +11084	643.818
  139.88 +11419	688.217
  139.89 +11476	688.784
  139.90 +11517	688.985
  139.91 +11752	717.832
  139.92 +11847	727.182
  139.93 +11867	726.529
  139.94 +11868	734.337
  139.95 +11953	732.28
  139.96 +11966	742.812
  139.97 +12140	756.818
  139.98 +12383	780.244
  139.99 +12433	816.963
 139.100 +12500	804.578
 139.101 +12578	802.743
 139.102 +12630	806.738
 139.103 +12666	808.474
 139.104 +12827	828.823
 139.105 +12962	841.036
 139.106 +12993	851.445
 139.107 +13034	851.426
 139.108 +13078	855.43
 139.109 +13713	927.174
 139.110 +13769	928.31
 139.111 +13966	954.907
 139.112 +14110	971.738
 139.113 +14203	976.326
 139.114 +15260	1108.17
 139.115 +15439	1132.28
 139.116 +15572	1154.65
 139.117 +15717	1167.33
 139.118 +15829	1181.8
 139.119 +15880	1191.49
 139.120 +15885	1195.2
 139.121 +15921	1199.02
 139.122 +15950	1199.69
 139.123 +16146	1222.97
 139.124 +16217	1235.66
 139.125 +16276	1250.55
 139.126 +16293	1257.41
 139.127 +16358	1258.08
 139.128 +16423	1255.02
 139.129 +16598	1278.18
 139.130 +16668	1290.93
 139.131 +16881	1344.48
 139.132 +16964	1326.39
 139.133 +17009	1329.8
 139.134 +17423	1390.28
 139.135 +17518	1407.57
 139.136 +17794	1437.97
 139.137 +17946	1470.18
 139.138 +18026	1481.86
 139.139 +18105	1497.08
 139.140 +18449	1553.36
 139.141 +18685	1578.3
 139.142 +18711	1572.14
 139.143 +18993	1647.71
 139.144 +19032	1620
 139.145 +19137	1668.46
 139.146 +19173	1632.03
 139.147 +19210	1654.32
 139.148 +19344	1672.77
 139.149 +19480	1687.57
 139.150 +19568	1701.33
 139.151 +19641	1729.73
 139.152 +19736	1724.86
 139.153 +19821	1745.81
   140.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   140.2 +++ b/randGraph/iso/vf2pIso10_1.txt	Tue Nov 22 08:15:16 2016 +0100
   140.3 @@ -0,0 +1,150 @@
   140.4 +371	1.11833
   140.5 +395	1.27867
   140.6 +817	3.766
   140.7 +896	4.23033
   140.8 +918	4.45167
   140.9 +993	5.03167
  140.10 +1130	6.16867
  140.11 +1209	6.77867
  140.12 +1227	6.961
  140.13 +1236	6.99767
  140.14 +1515	9.817
  140.15 +1601	10.9007
  140.16 +1623	11.1377
  140.17 +1693	11.9723
  140.18 +1719	12.327
  140.19 +1720	12.376
  140.20 +2046	17.1333
  140.21 +2273	19.9223
  140.22 +2397	22.19
  140.23 +2438	23.43
  140.24 +2469	23.3093
  140.25 +2484	23.485
  140.26 +2556	25.4357
  140.27 +2656	26.312
  140.28 +2678	26.7383
  140.29 +2697	27.8737
  140.30 +2761	28.1483
  140.31 +2776	28.6357
  140.32 +2828	30.2983
  140.33 +2921	31.2717
  140.34 +2992	32.5533
  140.35 +3116	36.2827
  140.36 +3198	36.915
  140.37 +3231	38.7797
  140.38 +3322	39.834
  140.39 +3325	39.5463
  140.40 +3381	40.8823
  140.41 +3391	41.656
  140.42 +3580	45.267
  140.43 +3643	46.4407
  140.44 +3775	50.0253
  140.45 +3803	50.2517
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  140.47 +4132	59.9083
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  140.62 +5501	99.8387
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  140.65 +6323	130.082
  140.66 +6363	130.893
  140.67 +6400	133.279
  140.68 +6725	145.988
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  140.70 +6828	152.555
  140.71 +7183	164.512
  140.72 +7189	167.359
  140.73 +7237	171.757
  140.74 +7582	182.968
  140.75 +7590	183.412
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  140.78 +8258	216.204
  140.79 +8784	242.524
  140.80 +8845	246.099
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  140.82 +9011	254.975
  140.83 +9012	253.78
  140.84 +9090	262.967
  140.85 +9732	294.994
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  140.88 +10313	338.256
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  140.91 +10871	366.195
  140.92 +11037	381.021
  140.93 +11214	396.272
  140.94 +11315	392.349
  140.95 +11466	406.025
  140.96 +11675	428.273
  140.97 +11792	428.912
  140.98 +11895	436.552
  140.99 +12011	452.611
 140.100 +12027	444.26
 140.101 +12215	454.918
 140.102 +12314	462.524
 140.103 +12332	466.498
 140.104 +12430	475.677
 140.105 +12496	486.519
 140.106 +12629	488.718
 140.107 +12815	503.275
 140.108 +12834	523.213
 140.109 +12928	511.078
 140.110 +13186	531.093
 140.111 +13354	544.274
 140.112 +13406	555.552
 140.113 +13482	557.669
 140.114 +13690	569.925
 140.115 +13921	587.318
 140.116 +13923	590.685
 140.117 +14052	610.82
 140.118 +14243	623.192
 140.119 +14309	634.848
 140.120 +14328	623.964
 140.121 +14369	644.294
 140.122 +14737	672.891
 140.123 +15239	701.649
 140.124 +15273	719.861
 140.125 +15284	708.873
 140.126 +15348	710.232
 140.127 +15908	772.151
 140.128 +16023	785.872
 140.129 +16133	789.249
 140.130 +16292	807.356
 140.131 +16499	831.314
 140.132 +16855	866.472
 140.133 +17320	906.521
 140.134 +18045	987.021
 140.135 +18086	992.404
 140.136 +18097	995.914
 140.137 +18107	1002.18
 140.138 +18301	1019.99
 140.139 +18330	1015.99
 140.140 +18395	1027.2
 140.141 +18478	1047.95
 140.142 +18538	1036.37
 140.143 +18551	1038.84
 140.144 +18563	1038.25
 140.145 +18616	1054.28
 140.146 +18650	1073.19
 140.147 +18815	1076.38
 140.148 +19241	1120.12
 140.149 +19360	1149.44
 140.150 +19364	1133.82
 140.151 +19636	1161.3
 140.152 +19642	1165.09
 140.153 +19907	1202.62
   141.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   141.2 +++ b/randGraph/iso/vf2pIso15_1.txt	Tue Nov 22 08:15:16 2016 +0100
   141.3 @@ -0,0 +1,150 @@
   141.4 +176	0.564333
   141.5 +201	0.680333
   141.6 +248	0.867
   141.7 +526	2.36667
   141.8 +773	4.571
   141.9 +909	5.37467
  141.10 +959	5.516
  141.11 +1023	6.28967
  141.12 +1048	6.43433
  141.13 +1186	7.972
  141.14 +1211	7.93233
  141.15 +1401	10.1643
  141.16 +1498	11.476
  141.17 +1557	12.0227
  141.18 +1696	15.4357
  141.19 +1732	14.1733
  141.20 +1747	14.9837
  141.21 +2030	18.6953
  141.22 +2056	19.0063
  141.23 +2172	20.641
  141.24 +2345	23.4693
  141.25 +2551	27.3363
  141.26 +2813	33.0293
  141.27 +2915	34.5197
  141.28 +2979	36.213
  141.29 +3450	46.0727
  141.30 +3497	47.4427
  141.31 +3626	50.8307
  141.32 +3660	51.666
  141.33 +3877	57.375
  141.34 +4246	67.732
  141.35 +4430	79.4417
  141.36 +4445	72.8763
  141.37 +4449	73.146
  141.38 +4734	82.0657
  141.39 +4961	88.574
  141.40 +5009	91.247
  141.41 +5109	93.131
  141.42 +5259	98.3897
  141.43 +5661	112.654
  141.44 +5722	115.168
  141.45 +5810	118.769
  141.46 +5836	118.441
  141.47 +5904	123.274
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  141.56 +7270	179.878
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  141.82 +11229	410.057
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 141.100 +13510	580.194
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 141.104 +14425	657.463
 141.105 +14767	690.373
 141.106 +15008	713.249
 141.107 +15062	712.821
 141.108 +15066	717.789
 141.109 +15105	724.236
 141.110 +15111	721.013
 141.111 +15134	777.968
 141.112 +15217	727.95
 141.113 +15493	754.124
 141.114 +15571	771.355
 141.115 +15631	781.681
 141.116 +15664	861.288
 141.117 +15957	861.274
 141.118 +16007	871.911
 141.119 +16026	812.203
 141.120 +16029	816.717
 141.121 +16171	827.481
 141.122 +16365	846.433
 141.123 +16432	849.503
 141.124 +16503	934.303
 141.125 +16614	864.238
 141.126 +16691	905.426
 141.127 +16714	878.326
 141.128 +16992	915.639
 141.129 +17014	914.313
 141.130 +17139	1025.43
 141.131 +17140	935.065
 141.132 +17163	930.383
 141.133 +17317	947.252
 141.134 +17362	976.425
 141.135 +17395	960.898
 141.136 +17637	999.306
 141.137 +17717	989.295
 141.138 +17953	1026.75
 141.139 +18103	1028.22
 141.140 +18150	1033.33
 141.141 +18198	1041.62
 141.142 +18201	1035.62
 141.143 +18244	1134.24
 141.144 +18263	1050.58
 141.145 +18711	1106.11
 141.146 +18740	1096.77
 141.147 +19082	1155.23
 141.148 +19175	1149.44
 141.149 +19205	1154.88
 141.150 +19546	1203.89
 141.151 +19571	1201.74
 141.152 +19790	1236.07
 141.153 +19849	1231
   142.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   142.2 +++ b/randGraph/iso/vf2pIso30_1.txt	Tue Nov 22 08:15:16 2016 +0100
   142.3 @@ -0,0 +1,78 @@
   142.4 +431	2.79433
   142.5 +1427	14.372
   142.6 +1907	21.9707
   142.7 +2207	27.3327
   142.8 +2821	40.378
   142.9 +2962	43.2867
  142.10 +3218	49.5623
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  142.12 +3789	64.7903
  142.13 +4318	81.121
  142.14 +4735	93.7133
  142.15 +5023	103.343
  142.16 +5039	103.272
  142.17 +5340	115.846
  142.18 +6476	163.966
  142.19 +6655	168.633
  142.20 +6880	178.643
  142.21 +7063	186.107
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  142.23 +7525	209.674
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  142.25 +7790	228.302
  142.26 +7926	231.419
  142.27 +8163	255.66
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  142.40 +11529	458.106
  142.41 +11578	470.117
  142.42 +11731	472.158
  142.43 +11828	480.679
  142.44 +11835	483.293
  142.45 +12073	499.352
  142.46 +12783	557.565
  142.47 +13286	596.93
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  142.49 +13594	636.049
  142.50 +13761	642.147
  142.51 +13907	650.99
  142.52 +14023	661.275
  142.53 +14090	673.737
  142.54 +14400	695.074
  142.55 +14476	701.143
  142.56 +14510	719.181
  142.57 +14761	736.055
  142.58 +15631	824.767
  142.59 +15829	836.491
  142.60 +16433	893.111
  142.61 +16642	924.982
  142.62 +16805	937.985
  142.63 +17136	966.686
  142.64 +17139	965.419
  142.65 +17211	980.675
  142.66 +17231	986.482
  142.67 +17455	1001.69
  142.68 +17748	1040.39
  142.69 +17871	1057.27
  142.70 +18307	1094.26
  142.71 +18432	1106.87
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  142.73 +18499	1117.88
  142.74 +18504	1136.65
  142.75 +18861	1156.82
  142.76 +18957	1176.25
  142.77 +19080	1209.36
  142.78 +19250	1217.55
  142.79 +19656	1257.58
  142.80 +19765	1272.94
  142.81 +19992	1309.2
   143.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   143.2 +++ b/randGraph/iso/vf2pIso35_1.txt	Tue Nov 22 08:15:16 2016 +0100
   143.3 @@ -0,0 +1,149 @@
   143.4 +26	0.091
   143.5 +442	3.31567
   143.6 +799	7.10933
   143.7 +912	8.28067
   143.8 +1000	9.53
   143.9 +1031	10.031
  143.10 +1034	10.117
  143.11 +1126	11.5307
  143.12 +1185	12.012
  143.13 +1256	13.194
  143.14 +1363	15.002
  143.15 +1461	16.0057
  143.16 +1550	17.4427
  143.17 +1569	17.7457
  143.18 +1602	18.6967
  143.19 +1678	19.6053
  143.20 +1882	23.043
  143.21 +2005	25.181
  143.22 +2190	28.9303
  143.23 +2238	29.904
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  143.25 +2291	31.069
  143.26 +2452	34.4053
  143.27 +2515	35.5033
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  143.29 +2602	37.4673
  143.30 +2704	40.017
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  143.33 +3056	52.3233
  143.34 +3254	54.81
  143.35 +3352	55.5863
  143.36 +3366	56.155
  143.37 +3418	57.559
  143.38 +3463	59.1837
  143.39 +3601	62.7903
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 143.101 +12700	567.36
 143.102 +12820	588.989
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 143.104 +12901	588.306
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 143.118 +14617	741.747
 143.119 +14770	784.292
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 143.121 +14913	766.362
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 143.126 +15950	870.279
 143.127 +16097	882.921
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 143.129 +16230	920.416
 143.130 +16324	912.497
 143.131 +16329	907.784
 143.132 +16342	910.341
 143.133 +16728	954.709
 143.134 +17286	1024.67
 143.135 +17405	1027.04
 143.136 +17468	1039.83
 143.137 +17619	1047.15
 143.138 +17625	1052.02
 143.139 +17840	1071.67
 143.140 +17870	1075.38
 143.141 +18250	1117.58
 143.142 +18612	1198.56
 143.143 +18616	1162.23
 143.144 +18655	1205.46
 143.145 +18951	1238.16
 143.146 +18980	1205.54
 143.147 +19122	1227.88
 143.148 +19285	1248.82
 143.149 +19311	1268.4
 143.150 +19523	1272.95
 143.151 +19743	1301.84
 143.152 +19862	1331.85
   144.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   144.2 +++ b/randGraph/iso/vf2pIso45_1.txt	Tue Nov 22 08:15:16 2016 +0100
   144.3 @@ -0,0 +1,150 @@
   144.4 +386	3.324
   144.5 +447	4.06567
   144.6 +519	4.81933
   144.7 +529	4.97867
   144.8 +573	5.57967
   144.9 +656	6.73867
  144.10 +666	6.672
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  144.13 +922	10.081
  144.14 +1000	11.2587
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  144.16 +1143	13.4053
  144.17 +1265	15.4557
  144.18 +1633	21.8493
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  144.25 +2717	45.6173
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  144.27 +3021	52.3687
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 144.103 +13444	661.455
 144.104 +13503	667.127
 144.105 +14053	719.333
 144.106 +14056	729.83
 144.107 +14132	749.617
 144.108 +14195	734.141
 144.109 +14242	735.271
 144.110 +14592	770.466
 144.111 +14882	797.771
 144.112 +14890	798.353
 144.113 +14946	811.182
 144.114 +14970	806.116
 144.115 +15017	812.877
 144.116 +15137	833.765
 144.117 +15331	852.753
 144.118 +15393	868.11
 144.119 +15717	908.828
 144.120 +16082	923.461
 144.121 +16279	952.989
 144.122 +16482	963.094
 144.123 +16497	979.317
 144.124 +16598	981.681
 144.125 +16791	998.893
 144.126 +16815	1004.67
 144.127 +16832	1010.97
 144.128 +16909	1033.43
 144.129 +16915	1012.6
 144.130 +17049	1033.48
 144.131 +17282	1063.13
 144.132 +17472	1085.4
 144.133 +17490	1083.74
 144.134 +17501	1077.6
 144.135 +17587	1101.97
 144.136 +17764	1131.28
 144.137 +17765	1119.24
 144.138 +17933	1139.88
 144.139 +18063	1141.84
 144.140 +18132	1160.64
 144.141 +18211	1166.42
 144.142 +18484	1202.17
 144.143 +18556	1219.2
 144.144 +18581	1212.34
 144.145 +18719	1250.32
 144.146 +18853	1239.53
 144.147 +18892	1260.8
 144.148 +18969	1264.25
 144.149 +19108	1296.38
 144.150 +19248	1295.03
 144.151 +19283	1303.22
 144.152 +19819	1375.7
 144.153 +19884	1380.73
   145.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   145.2 +++ b/randGraph/iso/vf2pIso5_1.txt	Tue Nov 22 08:15:16 2016 +0100
   145.3 @@ -0,0 +1,149 @@
   145.4 +109	0.160333
   145.5 +342	0.768667
   145.6 +463	1.176
   145.7 +796	2.82167
   145.8 +1084	4.669
   145.9 +1155	5.19067
  145.10 +1377	7.12367
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  145.12 +1549	8.769
  145.13 +1564	8.90367
  145.14 +1567	8.98333
  145.15 +1595	9.452
  145.16 +1607	9.49733
  145.17 +2002	13.988
  145.18 +2193	16.5057
  145.19 +2248	17.248
  145.20 +2426	20.7077
  145.21 +2447	20.219
  145.22 +2519	21.2823
  145.23 +2600	22.6427
  145.24 +2778	25.5963
  145.25 +2819	26.295
  145.26 +2832	26.4467
  145.27 +2836	27.649
  145.28 +2925	28.7703
  145.29 +3186	33.7007
  145.30 +3304	35.421
  145.31 +3565	40.941
  145.32 +3811	47.9227
  145.33 +3818	46.575
  145.34 +3854	47.4827
  145.35 +3961	49.8503
  145.36 +4301	59.711
  145.37 +4389	62.441
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  145.39 +4682	68.7103
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  145.90 +10076	310.629
  145.91 +10211	316.317
  145.92 +10370	325.568
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  145.96 +10802	354.166
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  145.99 +11130	367.137
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 145.101 +11273	384.08
 145.102 +11403	390.66
 145.103 +11937	420.697
 145.104 +11943	420.969
 145.105 +12050	428.333
 145.106 +12166	446.316
 145.107 +12173	437.183
 145.108 +12216	440.372
 145.109 +12220	449.09
 145.110 +12376	452.176
 145.111 +12451	456.736
 145.112 +12543	463.836
 145.113 +12663	484.274
 145.114 +12701	484.142
 145.115 +12703	475.083
 145.116 +12726	477.206
 145.117 +12768	480.049
 145.118 +12805	483.332
 145.119 +13279	519.868
 145.120 +13525	539.538
 145.121 +13575	541.517
 145.122 +13688	550.166
 145.123 +13785	558.028
 145.124 +13877	565.846
 145.125 +14088	588.459
 145.126 +14090	583.104
 145.127 +14251	608.133
 145.128 +14421	610.997
 145.129 +14465	613.764
 145.130 +14755	638.297
 145.131 +14975	656.8
 145.132 +15509	703.964
 145.133 +15731	738.788
 145.134 +15763	728.657
 145.135 +15770	742.474
 145.136 +15876	737.62
 145.137 +16011	766.746
 145.138 +16169	765.951
 145.139 +16342	802.882
 145.140 +16722	847.363
 145.141 +17001	870.866
 145.142 +17323	903.881
 145.143 +17432	896.281
 145.144 +17563	917.642
 145.145 +17913	966.674
 145.146 +18207	977.226
 145.147 +18532	1039.91
 145.148 +18722	1038.29
 145.149 +19169	1110.09
 145.150 +19372	1109.05
 145.151 +19430	1139.05
 145.152 +19499	1115.15
   146.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   146.2 +++ b/randGraph/iso/vf2pIso7_1.txt	Tue Nov 22 08:15:16 2016 +0100
   146.3 @@ -0,0 +1,30 @@
   146.4 +460	1.44967
   146.5 +1133	5.47133
   146.6 +1988	14.5803
   146.7 +2419	20.771
   146.8 +2865	28.3207
   146.9 +4604	68.6683
  146.10 +4770	73.1507
  146.11 +5861	116.754
  146.12 +6314	124.661
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  146.14 +7672	180.995
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  146.16 +9691	286.655
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  146.18 +10575	336.376
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  146.22 +13337	531.397
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  146.25 +14680	643.1
  146.26 +16107	773.629
  146.27 +16527	808.381
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  146.32 +19207	1098.73
  146.33 +19547	1133.21
   147.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   147.2 +++ b/randGraph/iso/vf2pIso80_1.txt	Tue Nov 22 08:15:16 2016 +0100
   147.3 @@ -0,0 +1,30 @@
   147.4 +460	7.11433
   147.5 +1133	20.6937
   147.6 +1988	43.029
   147.7 +2419	52.139
   147.8 +2865	68.0847
   147.9 +4604	131.703
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  147.21 +11871	651.784
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  147.32 +19207	1530.19
  147.33 +19547	1555.68
   148.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   148.2 +++ b/randGraph/iso/vf2ppIso.txt	Tue Nov 22 08:15:16 2016 +0100
   148.3 @@ -0,0 +1,149 @@
   148.4 +127	0.2475
   148.5 +162	0.3179
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   148.9 +491	1.0078
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 148.100 +13109	37.7132
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 148.127 +16841	49.0651
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 148.131 +17047	51.6072
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 148.139 +18160	55.594
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 148.141 +18347	52.5131
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 148.149 +19695	62.52
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 148.151 +19952	57.6225
 148.152 +19978	56.2806
   149.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   149.2 +++ b/randGraph/iso/vf2ppIso100_1.txt	Tue Nov 22 08:15:16 2016 +0100
   149.3 @@ -0,0 +1,150 @@
   149.4 +91	0.910333
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  149.22 +2743	51.2477
  149.23 +2835	50.488
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 149.104 +12827	340.896
 149.105 +12962	342.306
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 149.107 +13034	351.315
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 149.110 +13769	373.007
 149.111 +13966	379.592
 149.112 +14110	384.738
 149.113 +14203	379.43
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 149.116 +15572	441.33
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 149.118 +15829	444.319
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 149.120 +15885	454.421
 149.121 +15921	451.732
 149.122 +15950	451.867
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 149.124 +16217	461.736
 149.125 +16276	468.217
 149.126 +16293	462.08
 149.127 +16358	468.584
 149.128 +16423	468.44
 149.129 +16598	472.301
 149.130 +16668	475.421
 149.131 +16881	490.242
 149.132 +16964	486.617
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 149.134 +17423	500.609
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 149.139 +18105	532.395
 149.140 +18449	542.708
 149.141 +18685	549.002
 149.142 +18711	549.413
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 149.144 +19032	554.677
 149.145 +19137	571.891
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 149.147 +19210	564.167
 149.148 +19344	575.91
 149.149 +19480	573.341
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 149.151 +19641	585.854
 149.152 +19736	589.563
 149.153 +19821	587.744
   150.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   150.2 +++ b/randGraph/iso/vf2ppIso10_1.txt	Tue Nov 22 08:15:16 2016 +0100
   150.3 @@ -0,0 +1,150 @@
   150.4 +371	0.654667
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   150.9 +993	2.02267
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  150.14 +1515	3.02033
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  150.16 +1623	3.33867
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 150.128 +16023	43.0453
 150.129 +16133	42.662
 150.130 +16292	42.6583
 150.131 +16499	42.931
 150.132 +16855	44.4327
 150.133 +17320	46.7793
 150.134 +18045	47.5993
 150.135 +18086	46.5393
 150.136 +18097	46.7527
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 150.151 +19636	51.498
 150.152 +19642	54.0663
 150.153 +19907	52.0817
   151.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   151.2 +++ b/randGraph/iso/vf2ppIso15_1.txt	Tue Nov 22 08:15:16 2016 +0100
   151.3 @@ -0,0 +1,150 @@
   151.4 +176	0.438
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   151.8 +773	2.526
   151.9 +909	2.45967
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  151.13 +1186	3.466
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  151.15 +1401	4.10033
  151.16 +1498	4.508
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  151.26 +2813	9.07
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  151.34 +4246	14.0683
  151.35 +4430	16.5237
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 151.152 +19790	77.314
 151.153 +19849	82.4623
   152.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   152.2 +++ b/randGraph/iso/vf2ppIso30_1.txt	Tue Nov 22 08:15:16 2016 +0100
   152.3 @@ -0,0 +1,78 @@
   152.4 +431	1.97533
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  152.80 +19765	142.776
  152.81 +19992	147.166
   153.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   153.2 +++ b/randGraph/iso/vf2ppIso35_1.txt	Tue Nov 22 08:15:16 2016 +0100
   153.3 @@ -0,0 +1,149 @@
   153.4 +26	0.077
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 153.136 +17468	144.804
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 153.141 +18250	153.789
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 153.151 +19743	168.437
 153.152 +19862	175.334
   154.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   154.2 +++ b/randGraph/iso/vf2ppIso45_1.txt	Tue Nov 22 08:15:16 2016 +0100
   154.3 @@ -0,0 +1,150 @@
   154.4 +386	2.542
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 154.119 +15717	177.78
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 154.121 +16279	165.31
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 154.130 +17049	173.033
 154.131 +17282	176.967
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 154.149 +19108	205.495
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 154.152 +19819	220.642
 154.153 +19884	210.157
   155.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   155.2 +++ b/randGraph/iso/vf2ppIso5_1.txt	Tue Nov 22 08:15:16 2016 +0100
   155.3 @@ -0,0 +1,149 @@
   155.4 +109	0.118667
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 155.148 +18722	29.3833
 155.149 +19169	30.965
 155.150 +19372	29.9257
 155.151 +19430	31.733
 155.152 +19499	29.9433
   156.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   156.2 +++ b/randGraph/iso/vf2ppIso7_1.txt	Tue Nov 22 08:15:16 2016 +0100
   156.3 @@ -0,0 +1,30 @@
   156.4 +460	0.711667
   156.5 +1133	1.702
   156.6 +1988	3.14833
   156.7 +2419	3.95133
   156.8 +2865	4.776
   156.9 +4604	8.03
  156.10 +4770	8.35033
  156.11 +5861	11.282
  156.12 +6314	11.4307
  156.13 +7278	13.3083
  156.14 +7672	13.939
  156.15 +8665	16.2047
  156.16 +9691	18.14
  156.17 +10150	19.1327
  156.18 +10575	19.813
  156.19 +11432	21.7783
  156.20 +11832	22.9853
  156.21 +11871	22.8443
  156.22 +13337	25.7413
  156.23 +13880	26.926
  156.24 +14328	27.747
  156.25 +14680	28.3803
  156.26 +16107	31.4907
  156.27 +16527	32.504
  156.28 +17538	34.5537
  156.29 +18692	37.4403
  156.30 +18757	37.4073
  156.31 +19043	37.9937
  156.32 +19207	38.2977
  156.33 +19547	38.751
   157.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
   157.2 +++ b/randGraph/iso/vf2ppIso80_1.txt	Tue Nov 22 08:15:16 2016 +0100
   157.3 @@ -0,0 +1,30 @@
   157.4 +460	5.97667
   157.5 +1133	15.4167
   157.6 +1988	27.5997
   157.7 +2419	34.2267
   157.8 +2865	43.3543
   157.9 +4604	67.9797
  157.10 +4770	70.3437
  157.11 +5861	97.6497
  157.12 +6314	103.801
  157.13 +7278	123.768
  157.14 +7672	127.688
  157.15 +8665	159.771
  157.16 +9691	171.676
  157.17 +10150	181.881
  157.18 +10575	206.934
  157.19 +11432	230.12
  157.20 +11832	221.124
  157.21 +11871	222.772
  157.22 +13337	270.319
  157.23 +13880	272.756
  157.24 +14328	283.048
  157.25 +14680	295.872
  157.26 +16107	338.477
  157.27 +16527	345.87
  157.28 +17538	393.947
  157.29 +18692	425.632
  157.30 +18757	421.26
  157.31 +19043	417.752
  157.32 +19207	437.89
  157.33 +19547	433.38