lemon/concepts/graph.h
author Peter Kovacs <kpeter@inf.elte.hu>
Wed, 06 May 2009 14:46:05 +0200
changeset 649 76cbcb3e9bbb
parent 559 c5fd2d996909
child 657 bf7928412136
permissions -rw-r--r--
Add a test file for the connectivity functions (#285)
The Euler tools have a separate test file.
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library.
     4  *
     5  * Copyright (C) 2003-2009
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    18 
    19 ///\ingroup graph_concepts
    20 ///\file
    21 ///\brief The concept of Undirected Graphs.
    22 
    23 #ifndef LEMON_CONCEPTS_GRAPH_H
    24 #define LEMON_CONCEPTS_GRAPH_H
    25 
    26 #include <lemon/concepts/graph_components.h>
    27 #include <lemon/core.h>
    28 
    29 namespace lemon {
    30   namespace concepts {
    31 
    32     /// \ingroup graph_concepts
    33     ///
    34     /// \brief Class describing the concept of Undirected Graphs.
    35     ///
    36     /// This class describes the common interface of all Undirected
    37     /// Graphs.
    38     ///
    39     /// As all concept describing classes it provides only interface
    40     /// without any sensible implementation. So any algorithm for
    41     /// undirected graph should compile with this class, but it will not
    42     /// run properly, of course.
    43     ///
    44     /// The LEMON undirected graphs also fulfill the concept of
    45     /// directed graphs (\ref lemon::concepts::Digraph "Digraph
    46     /// Concept"). Each edges can be seen as two opposite
    47     /// directed arc and consequently the undirected graph can be
    48     /// seen as the direceted graph of these directed arcs. The
    49     /// Graph has the Edge inner class for the edges and
    50     /// the Arc type for the directed arcs. The Arc type is
    51     /// convertible to Edge or inherited from it so from a directed
    52     /// arc we can get the represented edge.
    53     ///
    54     /// In the sense of the LEMON each edge has a default
    55     /// direction (it should be in every computer implementation,
    56     /// because the order of edge's nodes defines an
    57     /// orientation). With the default orientation we can define that
    58     /// the directed arc is forward or backward directed. With the \c
    59     /// direction() and \c direct() function we can get the direction
    60     /// of the directed arc and we can direct an edge.
    61     ///
    62     /// The EdgeIt is an iterator for the edges. We can use
    63     /// the EdgeMap to map values for the edges. The InArcIt and
    64     /// OutArcIt iterates on the same edges but with opposite
    65     /// direction. The IncEdgeIt iterates also on the same edges
    66     /// as the OutArcIt and InArcIt but it is not convertible to Arc just
    67     /// to Edge.
    68     class Graph {
    69     public:
    70       /// \brief The undirected graph should be tagged by the
    71       /// UndirectedTag.
    72       ///
    73       /// The undirected graph should be tagged by the UndirectedTag. This
    74       /// tag helps the enable_if technics to make compile time
    75       /// specializations for undirected graphs.
    76       typedef True UndirectedTag;
    77 
    78       /// \brief The base type of node iterators,
    79       /// or in other words, the trivial node iterator.
    80       ///
    81       /// This is the base type of each node iterator,
    82       /// thus each kind of node iterator converts to this.
    83       /// More precisely each kind of node iterator should be inherited
    84       /// from the trivial node iterator.
    85       class Node {
    86       public:
    87         /// Default constructor
    88 
    89         /// @warning The default constructor sets the iterator
    90         /// to an undefined value.
    91         Node() { }
    92         /// Copy constructor.
    93 
    94         /// Copy constructor.
    95         ///
    96         Node(const Node&) { }
    97 
    98         /// Invalid constructor \& conversion.
    99 
   100         /// This constructor initializes the iterator to be invalid.
   101         /// \sa Invalid for more details.
   102         Node(Invalid) { }
   103         /// Equality operator
   104 
   105         /// Two iterators are equal if and only if they point to the
   106         /// same object or both are invalid.
   107         bool operator==(Node) const { return true; }
   108 
   109         /// Inequality operator
   110 
   111         /// \sa operator==(Node n)
   112         ///
   113         bool operator!=(Node) const { return true; }
   114 
   115         /// Artificial ordering operator.
   116 
   117         /// To allow the use of graph descriptors as key type in std::map or
   118         /// similar associative container we require this.
   119         ///
   120         /// \note This operator only have to define some strict ordering of
   121         /// the items; this order has nothing to do with the iteration
   122         /// ordering of the items.
   123         bool operator<(Node) const { return false; }
   124 
   125       };
   126 
   127       /// This iterator goes through each node.
   128 
   129       /// This iterator goes through each node.
   130       /// Its usage is quite simple, for example you can count the number
   131       /// of nodes in graph \c g of type \c Graph like this:
   132       ///\code
   133       /// int count=0;
   134       /// for (Graph::NodeIt n(g); n!=INVALID; ++n) ++count;
   135       ///\endcode
   136       class NodeIt : public Node {
   137       public:
   138         /// Default constructor
   139 
   140         /// @warning The default constructor sets the iterator
   141         /// to an undefined value.
   142         NodeIt() { }
   143         /// Copy constructor.
   144 
   145         /// Copy constructor.
   146         ///
   147         NodeIt(const NodeIt& n) : Node(n) { }
   148         /// Invalid constructor \& conversion.
   149 
   150         /// Initialize the iterator to be invalid.
   151         /// \sa Invalid for more details.
   152         NodeIt(Invalid) { }
   153         /// Sets the iterator to the first node.
   154 
   155         /// Sets the iterator to the first node of \c g.
   156         ///
   157         NodeIt(const Graph&) { }
   158         /// Node -> NodeIt conversion.
   159 
   160         /// Sets the iterator to the node of \c the graph pointed by
   161         /// the trivial iterator.
   162         /// This feature necessitates that each time we
   163         /// iterate the arc-set, the iteration order is the same.
   164         NodeIt(const Graph&, const Node&) { }
   165         /// Next node.
   166 
   167         /// Assign the iterator to the next node.
   168         ///
   169         NodeIt& operator++() { return *this; }
   170       };
   171 
   172 
   173       /// The base type of the edge iterators.
   174 
   175       /// The base type of the edge iterators.
   176       ///
   177       class Edge {
   178       public:
   179         /// Default constructor
   180 
   181         /// @warning The default constructor sets the iterator
   182         /// to an undefined value.
   183         Edge() { }
   184         /// Copy constructor.
   185 
   186         /// Copy constructor.
   187         ///
   188         Edge(const Edge&) { }
   189         /// Initialize the iterator to be invalid.
   190 
   191         /// Initialize the iterator to be invalid.
   192         ///
   193         Edge(Invalid) { }
   194         /// Equality operator
   195 
   196         /// Two iterators are equal if and only if they point to the
   197         /// same object or both are invalid.
   198         bool operator==(Edge) const { return true; }
   199         /// Inequality operator
   200 
   201         /// \sa operator==(Edge n)
   202         ///
   203         bool operator!=(Edge) const { return true; }
   204 
   205         /// Artificial ordering operator.
   206 
   207         /// To allow the use of graph descriptors as key type in std::map or
   208         /// similar associative container we require this.
   209         ///
   210         /// \note This operator only have to define some strict ordering of
   211         /// the items; this order has nothing to do with the iteration
   212         /// ordering of the items.
   213         bool operator<(Edge) const { return false; }
   214       };
   215 
   216       /// This iterator goes through each edge.
   217 
   218       /// This iterator goes through each edge of a graph.
   219       /// Its usage is quite simple, for example you can count the number
   220       /// of edges in a graph \c g of type \c Graph as follows:
   221       ///\code
   222       /// int count=0;
   223       /// for(Graph::EdgeIt e(g); e!=INVALID; ++e) ++count;
   224       ///\endcode
   225       class EdgeIt : public Edge {
   226       public:
   227         /// Default constructor
   228 
   229         /// @warning The default constructor sets the iterator
   230         /// to an undefined value.
   231         EdgeIt() { }
   232         /// Copy constructor.
   233 
   234         /// Copy constructor.
   235         ///
   236         EdgeIt(const EdgeIt& e) : Edge(e) { }
   237         /// Initialize the iterator to be invalid.
   238 
   239         /// Initialize the iterator to be invalid.
   240         ///
   241         EdgeIt(Invalid) { }
   242         /// This constructor sets the iterator to the first edge.
   243 
   244         /// This constructor sets the iterator to the first edge.
   245         EdgeIt(const Graph&) { }
   246         /// Edge -> EdgeIt conversion
   247 
   248         /// Sets the iterator to the value of the trivial iterator.
   249         /// This feature necessitates that each time we
   250         /// iterate the edge-set, the iteration order is the
   251         /// same.
   252         EdgeIt(const Graph&, const Edge&) { }
   253         /// Next edge
   254 
   255         /// Assign the iterator to the next edge.
   256         EdgeIt& operator++() { return *this; }
   257       };
   258 
   259       /// \brief This iterator goes trough the incident undirected
   260       /// arcs of a node.
   261       ///
   262       /// This iterator goes trough the incident edges
   263       /// of a certain node of a graph. You should assume that the
   264       /// loop arcs will be iterated twice.
   265       ///
   266       /// Its usage is quite simple, for example you can compute the
   267       /// degree (i.e. count the number of incident arcs of a node \c n
   268       /// in graph \c g of type \c Graph as follows.
   269       ///
   270       ///\code
   271       /// int count=0;
   272       /// for(Graph::IncEdgeIt e(g, n); e!=INVALID; ++e) ++count;
   273       ///\endcode
   274       class IncEdgeIt : public Edge {
   275       public:
   276         /// Default constructor
   277 
   278         /// @warning The default constructor sets the iterator
   279         /// to an undefined value.
   280         IncEdgeIt() { }
   281         /// Copy constructor.
   282 
   283         /// Copy constructor.
   284         ///
   285         IncEdgeIt(const IncEdgeIt& e) : Edge(e) { }
   286         /// Initialize the iterator to be invalid.
   287 
   288         /// Initialize the iterator to be invalid.
   289         ///
   290         IncEdgeIt(Invalid) { }
   291         /// This constructor sets the iterator to first incident arc.
   292 
   293         /// This constructor set the iterator to the first incident arc of
   294         /// the node.
   295         IncEdgeIt(const Graph&, const Node&) { }
   296         /// Edge -> IncEdgeIt conversion
   297 
   298         /// Sets the iterator to the value of the trivial iterator \c e.
   299         /// This feature necessitates that each time we
   300         /// iterate the arc-set, the iteration order is the same.
   301         IncEdgeIt(const Graph&, const Edge&) { }
   302         /// Next incident arc
   303 
   304         /// Assign the iterator to the next incident arc
   305         /// of the corresponding node.
   306         IncEdgeIt& operator++() { return *this; }
   307       };
   308 
   309       /// The directed arc type.
   310 
   311       /// The directed arc type. It can be converted to the
   312       /// edge or it should be inherited from the undirected
   313       /// arc.
   314       class Arc : public Edge {
   315       public:
   316         /// Default constructor
   317 
   318         /// @warning The default constructor sets the iterator
   319         /// to an undefined value.
   320         Arc() { }
   321         /// Copy constructor.
   322 
   323         /// Copy constructor.
   324         ///
   325         Arc(const Arc& e) : Edge(e) { }
   326         /// Initialize the iterator to be invalid.
   327 
   328         /// Initialize the iterator to be invalid.
   329         ///
   330         Arc(Invalid) { }
   331         /// Equality operator
   332 
   333         /// Two iterators are equal if and only if they point to the
   334         /// same object or both are invalid.
   335         bool operator==(Arc) const { return true; }
   336         /// Inequality operator
   337 
   338         /// \sa operator==(Arc n)
   339         ///
   340         bool operator!=(Arc) const { return true; }
   341 
   342         /// Artificial ordering operator.
   343 
   344         /// To allow the use of graph descriptors as key type in std::map or
   345         /// similar associative container we require this.
   346         ///
   347         /// \note This operator only have to define some strict ordering of
   348         /// the items; this order has nothing to do with the iteration
   349         /// ordering of the items.
   350         bool operator<(Arc) const { return false; }
   351 
   352       };
   353       /// This iterator goes through each directed arc.
   354 
   355       /// This iterator goes through each arc of a graph.
   356       /// Its usage is quite simple, for example you can count the number
   357       /// of arcs in a graph \c g of type \c Graph as follows:
   358       ///\code
   359       /// int count=0;
   360       /// for(Graph::ArcIt e(g); e!=INVALID; ++e) ++count;
   361       ///\endcode
   362       class ArcIt : public Arc {
   363       public:
   364         /// Default constructor
   365 
   366         /// @warning The default constructor sets the iterator
   367         /// to an undefined value.
   368         ArcIt() { }
   369         /// Copy constructor.
   370 
   371         /// Copy constructor.
   372         ///
   373         ArcIt(const ArcIt& e) : Arc(e) { }
   374         /// Initialize the iterator to be invalid.
   375 
   376         /// Initialize the iterator to be invalid.
   377         ///
   378         ArcIt(Invalid) { }
   379         /// This constructor sets the iterator to the first arc.
   380 
   381         /// This constructor sets the iterator to the first arc of \c g.
   382         ///@param g the graph
   383         ArcIt(const Graph &g) { ignore_unused_variable_warning(g); }
   384         /// Arc -> ArcIt conversion
   385 
   386         /// Sets the iterator to the value of the trivial iterator \c e.
   387         /// This feature necessitates that each time we
   388         /// iterate the arc-set, the iteration order is the same.
   389         ArcIt(const Graph&, const Arc&) { }
   390         ///Next arc
   391 
   392         /// Assign the iterator to the next arc.
   393         ArcIt& operator++() { return *this; }
   394       };
   395 
   396       /// This iterator goes trough the outgoing directed arcs of a node.
   397 
   398       /// This iterator goes trough the \e outgoing arcs of a certain node
   399       /// of a graph.
   400       /// Its usage is quite simple, for example you can count the number
   401       /// of outgoing arcs of a node \c n
   402       /// in graph \c g of type \c Graph as follows.
   403       ///\code
   404       /// int count=0;
   405       /// for (Graph::OutArcIt e(g, n); e!=INVALID; ++e) ++count;
   406       ///\endcode
   407 
   408       class OutArcIt : public Arc {
   409       public:
   410         /// Default constructor
   411 
   412         /// @warning The default constructor sets the iterator
   413         /// to an undefined value.
   414         OutArcIt() { }
   415         /// Copy constructor.
   416 
   417         /// Copy constructor.
   418         ///
   419         OutArcIt(const OutArcIt& e) : Arc(e) { }
   420         /// Initialize the iterator to be invalid.
   421 
   422         /// Initialize the iterator to be invalid.
   423         ///
   424         OutArcIt(Invalid) { }
   425         /// This constructor sets the iterator to the first outgoing arc.
   426 
   427         /// This constructor sets the iterator to the first outgoing arc of
   428         /// the node.
   429         ///@param n the node
   430         ///@param g the graph
   431         OutArcIt(const Graph& n, const Node& g) {
   432           ignore_unused_variable_warning(n);
   433           ignore_unused_variable_warning(g);
   434         }
   435         /// Arc -> OutArcIt conversion
   436 
   437         /// Sets the iterator to the value of the trivial iterator.
   438         /// This feature necessitates that each time we
   439         /// iterate the arc-set, the iteration order is the same.
   440         OutArcIt(const Graph&, const Arc&) { }
   441         ///Next outgoing arc
   442 
   443         /// Assign the iterator to the next
   444         /// outgoing arc of the corresponding node.
   445         OutArcIt& operator++() { return *this; }
   446       };
   447 
   448       /// This iterator goes trough the incoming directed arcs of a node.
   449 
   450       /// This iterator goes trough the \e incoming arcs of a certain node
   451       /// of a graph.
   452       /// Its usage is quite simple, for example you can count the number
   453       /// of outgoing arcs of a node \c n
   454       /// in graph \c g of type \c Graph as follows.
   455       ///\code
   456       /// int count=0;
   457       /// for(Graph::InArcIt e(g, n); e!=INVALID; ++e) ++count;
   458       ///\endcode
   459 
   460       class InArcIt : public Arc {
   461       public:
   462         /// Default constructor
   463 
   464         /// @warning The default constructor sets the iterator
   465         /// to an undefined value.
   466         InArcIt() { }
   467         /// Copy constructor.
   468 
   469         /// Copy constructor.
   470         ///
   471         InArcIt(const InArcIt& e) : Arc(e) { }
   472         /// Initialize the iterator to be invalid.
   473 
   474         /// Initialize the iterator to be invalid.
   475         ///
   476         InArcIt(Invalid) { }
   477         /// This constructor sets the iterator to first incoming arc.
   478 
   479         /// This constructor set the iterator to the first incoming arc of
   480         /// the node.
   481         ///@param n the node
   482         ///@param g the graph
   483         InArcIt(const Graph& g, const Node& n) {
   484           ignore_unused_variable_warning(n);
   485           ignore_unused_variable_warning(g);
   486         }
   487         /// Arc -> InArcIt conversion
   488 
   489         /// Sets the iterator to the value of the trivial iterator \c e.
   490         /// This feature necessitates that each time we
   491         /// iterate the arc-set, the iteration order is the same.
   492         InArcIt(const Graph&, const Arc&) { }
   493         /// Next incoming arc
   494 
   495         /// Assign the iterator to the next inarc of the corresponding node.
   496         ///
   497         InArcIt& operator++() { return *this; }
   498       };
   499 
   500       /// \brief Reference map of the nodes to type \c T.
   501       ///
   502       /// Reference map of the nodes to type \c T.
   503       template<class T>
   504       class NodeMap : public ReferenceMap<Node, T, T&, const T&>
   505       {
   506       public:
   507 
   508         ///\e
   509         NodeMap(const Graph&) { }
   510         ///\e
   511         NodeMap(const Graph&, T) { }
   512 
   513       private:
   514         ///Copy constructor
   515         NodeMap(const NodeMap& nm) :
   516           ReferenceMap<Node, T, T&, const T&>(nm) { }
   517         ///Assignment operator
   518         template <typename CMap>
   519         NodeMap& operator=(const CMap&) {
   520           checkConcept<ReadMap<Node, T>, CMap>();
   521           return *this;
   522         }
   523       };
   524 
   525       /// \brief Reference map of the arcs to type \c T.
   526       ///
   527       /// Reference map of the arcs to type \c T.
   528       template<class T>
   529       class ArcMap : public ReferenceMap<Arc, T, T&, const T&>
   530       {
   531       public:
   532 
   533         ///\e
   534         ArcMap(const Graph&) { }
   535         ///\e
   536         ArcMap(const Graph&, T) { }
   537       private:
   538         ///Copy constructor
   539         ArcMap(const ArcMap& em) :
   540           ReferenceMap<Arc, T, T&, const T&>(em) { }
   541         ///Assignment operator
   542         template <typename CMap>
   543         ArcMap& operator=(const CMap&) {
   544           checkConcept<ReadMap<Arc, T>, CMap>();
   545           return *this;
   546         }
   547       };
   548 
   549       /// Reference map of the edges to type \c T.
   550 
   551       /// Reference map of the edges to type \c T.
   552       template<class T>
   553       class EdgeMap : public ReferenceMap<Edge, T, T&, const T&>
   554       {
   555       public:
   556 
   557         ///\e
   558         EdgeMap(const Graph&) { }
   559         ///\e
   560         EdgeMap(const Graph&, T) { }
   561       private:
   562         ///Copy constructor
   563         EdgeMap(const EdgeMap& em) :
   564           ReferenceMap<Edge, T, T&, const T&>(em) {}
   565         ///Assignment operator
   566         template <typename CMap>
   567         EdgeMap& operator=(const CMap&) {
   568           checkConcept<ReadMap<Edge, T>, CMap>();
   569           return *this;
   570         }
   571       };
   572 
   573       /// \brief Direct the given edge.
   574       ///
   575       /// Direct the given edge. The returned arc source
   576       /// will be the given node.
   577       Arc direct(const Edge&, const Node&) const {
   578         return INVALID;
   579       }
   580 
   581       /// \brief Direct the given edge.
   582       ///
   583       /// Direct the given edge. The returned arc
   584       /// represents the given edge and the direction comes
   585       /// from the bool parameter. The source of the edge and
   586       /// the directed arc is the same when the given bool is true.
   587       Arc direct(const Edge&, bool) const {
   588         return INVALID;
   589       }
   590 
   591       /// \brief Returns true if the arc has default orientation.
   592       ///
   593       /// Returns whether the given directed arc is same orientation as
   594       /// the corresponding edge's default orientation.
   595       bool direction(Arc) const { return true; }
   596 
   597       /// \brief Returns the opposite directed arc.
   598       ///
   599       /// Returns the opposite directed arc.
   600       Arc oppositeArc(Arc) const { return INVALID; }
   601 
   602       /// \brief Opposite node on an arc
   603       ///
   604       /// \return The opposite of the given node on the given edge.
   605       Node oppositeNode(Node, Edge) const { return INVALID; }
   606 
   607       /// \brief First node of the edge.
   608       ///
   609       /// \return The first node of the given edge.
   610       ///
   611       /// Naturally edges don't have direction and thus
   612       /// don't have source and target node. However we use \c u() and \c v()
   613       /// methods to query the two nodes of the arc. The direction of the
   614       /// arc which arises this way is called the inherent direction of the
   615       /// edge, and is used to define the "default" direction
   616       /// of the directed versions of the arcs.
   617       /// \sa v()
   618       /// \sa direction()
   619       Node u(Edge) const { return INVALID; }
   620 
   621       /// \brief Second node of the edge.
   622       ///
   623       /// \return The second node of the given edge.
   624       ///
   625       /// Naturally edges don't have direction and thus
   626       /// don't have source and target node. However we use \c u() and \c v()
   627       /// methods to query the two nodes of the arc. The direction of the
   628       /// arc which arises this way is called the inherent direction of the
   629       /// edge, and is used to define the "default" direction
   630       /// of the directed versions of the arcs.
   631       /// \sa u()
   632       /// \sa direction()
   633       Node v(Edge) const { return INVALID; }
   634 
   635       /// \brief Source node of the directed arc.
   636       Node source(Arc) const { return INVALID; }
   637 
   638       /// \brief Target node of the directed arc.
   639       Node target(Arc) const { return INVALID; }
   640 
   641       /// \brief Returns the id of the node.
   642       int id(Node) const { return -1; }
   643 
   644       /// \brief Returns the id of the edge.
   645       int id(Edge) const { return -1; }
   646 
   647       /// \brief Returns the id of the arc.
   648       int id(Arc) const { return -1; }
   649 
   650       /// \brief Returns the node with the given id.
   651       ///
   652       /// \pre The argument should be a valid node id in the graph.
   653       Node nodeFromId(int) const { return INVALID; }
   654 
   655       /// \brief Returns the edge with the given id.
   656       ///
   657       /// \pre The argument should be a valid edge id in the graph.
   658       Edge edgeFromId(int) const { return INVALID; }
   659 
   660       /// \brief Returns the arc with the given id.
   661       ///
   662       /// \pre The argument should be a valid arc id in the graph.
   663       Arc arcFromId(int) const { return INVALID; }
   664 
   665       /// \brief Returns an upper bound on the node IDs.
   666       int maxNodeId() const { return -1; }
   667 
   668       /// \brief Returns an upper bound on the edge IDs.
   669       int maxEdgeId() const { return -1; }
   670 
   671       /// \brief Returns an upper bound on the arc IDs.
   672       int maxArcId() const { return -1; }
   673 
   674       void first(Node&) const {}
   675       void next(Node&) const {}
   676 
   677       void first(Edge&) const {}
   678       void next(Edge&) const {}
   679 
   680       void first(Arc&) const {}
   681       void next(Arc&) const {}
   682 
   683       void firstOut(Arc&, Node) const {}
   684       void nextOut(Arc&) const {}
   685 
   686       void firstIn(Arc&, Node) const {}
   687       void nextIn(Arc&) const {}
   688 
   689       void firstInc(Edge &, bool &, const Node &) const {}
   690       void nextInc(Edge &, bool &) const {}
   691 
   692       // The second parameter is dummy.
   693       Node fromId(int, Node) const { return INVALID; }
   694       // The second parameter is dummy.
   695       Edge fromId(int, Edge) const { return INVALID; }
   696       // The second parameter is dummy.
   697       Arc fromId(int, Arc) const { return INVALID; }
   698 
   699       // Dummy parameter.
   700       int maxId(Node) const { return -1; }
   701       // Dummy parameter.
   702       int maxId(Edge) const { return -1; }
   703       // Dummy parameter.
   704       int maxId(Arc) const { return -1; }
   705 
   706       /// \brief Base node of the iterator
   707       ///
   708       /// Returns the base node (the source in this case) of the iterator
   709       Node baseNode(OutArcIt e) const {
   710         return source(e);
   711       }
   712       /// \brief Running node of the iterator
   713       ///
   714       /// Returns the running node (the target in this case) of the
   715       /// iterator
   716       Node runningNode(OutArcIt e) const {
   717         return target(e);
   718       }
   719 
   720       /// \brief Base node of the iterator
   721       ///
   722       /// Returns the base node (the target in this case) of the iterator
   723       Node baseNode(InArcIt e) const {
   724         return target(e);
   725       }
   726       /// \brief Running node of the iterator
   727       ///
   728       /// Returns the running node (the source in this case) of the
   729       /// iterator
   730       Node runningNode(InArcIt e) const {
   731         return source(e);
   732       }
   733 
   734       /// \brief Base node of the iterator
   735       ///
   736       /// Returns the base node of the iterator
   737       Node baseNode(IncEdgeIt) const {
   738         return INVALID;
   739       }
   740 
   741       /// \brief Running node of the iterator
   742       ///
   743       /// Returns the running node of the iterator
   744       Node runningNode(IncEdgeIt) const {
   745         return INVALID;
   746       }
   747 
   748       template <typename _Graph>
   749       struct Constraints {
   750         void constraints() {
   751           checkConcept<BaseGraphComponent, _Graph>();
   752           checkConcept<IterableGraphComponent<>, _Graph>();
   753           checkConcept<IDableGraphComponent<>, _Graph>();
   754           checkConcept<MappableGraphComponent<>, _Graph>();
   755         }
   756       };
   757 
   758     };
   759 
   760   }
   761 
   762 }
   763 
   764 #endif