COIN-OR::LEMON - Graph Library

source: lemon/lemon/concepts/graph.h @ 833:e20173729589

Last change on this file since 833:e20173729589 was 833:e20173729589, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Small doc fixes in several files (#331)

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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/concepts/maps.h>
28#include <lemon/concept_check.h>
29#include <lemon/core.h>
30
31namespace lemon {
32  namespace concepts {
33
34    /// \ingroup graph_concepts
35    ///
36    /// \brief Class describing the concept of undirected graphs.
37    ///
38    /// This class describes the common interface of all undirected
39    /// graphs.
40    ///
41    /// Like all concept classes, it only provides an interface
42    /// without any sensible implementation. So any general algorithm for
43    /// undirected graphs should compile with this class, but it will not
44    /// run properly, of course.
45    /// An actual graph implementation like \ref ListGraph or
46    /// \ref SmartGraph may have additional functionality.   
47    ///
48    /// The undirected graphs also fulfill the concept of \ref Digraph
49    /// "directed graphs", since each edge can also be regarded as two
50    /// oppositely directed arcs.
51    /// Undirected graphs provide an Edge type for the undirected edges and
52    /// an Arc type for the directed arcs. The Arc type is convertible to
53    /// Edge or inherited from it, i.e. the corresponding edge can be
54    /// obtained from an arc.
55    /// EdgeIt and EdgeMap classes can be used for the edges, while ArcIt
56    /// and ArcMap classes can be used for the arcs (just like in digraphs).
57    /// Both InArcIt and OutArcIt iterates on the same edges but with
58    /// opposite direction. IncEdgeIt also iterates on the same edges
59    /// as OutArcIt and InArcIt, but it is not convertible to Arc,
60    /// only to Edge.
61    ///
62    /// In LEMON, each undirected edge has an inherent orientation.
63    /// Thus it can defined if an arc is forward or backward oriented in
64    /// an undirected graph with respect to this default oriantation of
65    /// the represented edge.
66    /// With the direction() and direct() functions the direction
67    /// of an arc can be obtained and set, respectively.
68    ///
69    /// Only nodes and edges can be added to or removed from an undirected
70    /// graph and the corresponding arcs are added or removed automatically.
71    ///
72    /// \sa Digraph
73    class Graph {
74    private:
75      /// Graphs are \e not copy constructible. Use DigraphCopy instead.
76      Graph(const Graph&) {}
77      /// \brief Assignment of a graph to another one is \e not allowed.
78      /// Use DigraphCopy instead.
79      void operator=(const Graph&) {}
80
81    public:
82      /// Default constructor.
83      Graph() {}
84
85      /// \brief Undirected graphs should be tagged with \c UndirectedTag.
86      ///
87      /// Undirected graphs should be tagged with \c UndirectedTag.
88      ///
89      /// This tag helps the \c enable_if technics to make compile time
90      /// specializations for undirected graphs.
91      typedef True UndirectedTag;
92
93      /// The node type of the graph
94
95      /// This class identifies a node of the graph. It also serves
96      /// as a base class of the node iterators,
97      /// thus they convert to this type.
98      class Node {
99      public:
100        /// Default constructor
101
102        /// Default constructor.
103        /// \warning It sets the object to an undefined value.
104        Node() { }
105        /// Copy constructor.
106
107        /// Copy constructor.
108        ///
109        Node(const Node&) { }
110
111        /// %Invalid constructor \& conversion.
112
113        /// Initializes the object to be invalid.
114        /// \sa Invalid for more details.
115        Node(Invalid) { }
116        /// Equality operator
117
118        /// Equality operator.
119        ///
120        /// Two iterators are equal if and only if they point to the
121        /// same object or both are \c INVALID.
122        bool operator==(Node) const { return true; }
123
124        /// Inequality operator
125
126        /// Inequality operator.
127        bool operator!=(Node) const { return true; }
128
129        /// Artificial ordering operator.
130
131        /// Artificial ordering operator.
132        ///
133        /// \note This operator only has to define some strict ordering of
134        /// the items; this order has nothing to do with the iteration
135        /// ordering of the items.
136        bool operator<(Node) const { return false; }
137
138      };
139
140      /// Iterator class for the nodes.
141
142      /// This iterator goes through each node of the graph.
143      /// Its usage is quite simple, for example, you can count the number
144      /// of nodes in a graph \c g of type \c %Graph like this:
145      ///\code
146      /// int count=0;
147      /// for (Graph::NodeIt n(g); n!=INVALID; ++n) ++count;
148      ///\endcode
149      class NodeIt : public Node {
150      public:
151        /// Default constructor
152
153        /// Default constructor.
154        /// \warning It sets the iterator to an undefined value.
155        NodeIt() { }
156        /// Copy constructor.
157
158        /// Copy constructor.
159        ///
160        NodeIt(const NodeIt& n) : Node(n) { }
161        /// %Invalid constructor \& conversion.
162
163        /// Initializes the iterator to be invalid.
164        /// \sa Invalid for more details.
165        NodeIt(Invalid) { }
166        /// Sets the iterator to the first node.
167
168        /// Sets the iterator to the first node of the given digraph.
169        ///
170        explicit NodeIt(const Graph&) { }
171        /// Sets the iterator to the given node.
172
173        /// Sets the iterator to the given node of the given digraph.
174        ///
175        NodeIt(const Graph&, const Node&) { }
176        /// Next node.
177
178        /// Assign the iterator to the next node.
179        ///
180        NodeIt& operator++() { return *this; }
181      };
182
183
184      /// The edge type of the graph
185
186      /// This class identifies an edge of the graph. It also serves
187      /// as a base class of the edge iterators,
188      /// thus they will convert to this type.
189      class Edge {
190      public:
191        /// Default constructor
192
193        /// Default constructor.
194        /// \warning It sets the object to an undefined value.
195        Edge() { }
196        /// Copy constructor.
197
198        /// Copy constructor.
199        ///
200        Edge(const Edge&) { }
201        /// %Invalid constructor \& conversion.
202
203        /// Initializes the object to be invalid.
204        /// \sa Invalid for more details.
205        Edge(Invalid) { }
206        /// Equality operator
207
208        /// Equality operator.
209        ///
210        /// Two iterators are equal if and only if they point to the
211        /// same object or both are \c INVALID.
212        bool operator==(Edge) const { return true; }
213        /// Inequality operator
214
215        /// Inequality operator.
216        bool operator!=(Edge) const { return true; }
217
218        /// Artificial ordering operator.
219
220        /// Artificial ordering operator.
221        ///
222        /// \note This operator only has to define some strict ordering of
223        /// the edges; this order has nothing to do with the iteration
224        /// ordering of the edges.
225        bool operator<(Edge) const { return false; }
226      };
227
228      /// Iterator class for the edges.
229
230      /// This iterator goes through each edge of the graph.
231      /// Its usage is quite simple, for example, you can count the number
232      /// of edges in a graph \c g of type \c %Graph as follows:
233      ///\code
234      /// int count=0;
235      /// for(Graph::EdgeIt e(g); e!=INVALID; ++e) ++count;
236      ///\endcode
237      class EdgeIt : public Edge {
238      public:
239        /// Default constructor
240
241        /// Default constructor.
242        /// \warning It sets the iterator to an undefined value.
243        EdgeIt() { }
244        /// Copy constructor.
245
246        /// Copy constructor.
247        ///
248        EdgeIt(const EdgeIt& e) : Edge(e) { }
249        /// %Invalid constructor \& conversion.
250
251        /// Initializes the iterator to be invalid.
252        /// \sa Invalid for more details.
253        EdgeIt(Invalid) { }
254        /// Sets the iterator to the first edge.
255
256        /// Sets the iterator to the first edge of the given graph.
257        ///
258        explicit EdgeIt(const Graph&) { }
259        /// Sets the iterator to the given edge.
260
261        /// Sets the iterator to the given edge of the given graph.
262        ///
263        EdgeIt(const Graph&, const Edge&) { }
264        /// Next edge
265
266        /// Assign the iterator to the next edge.
267        ///
268        EdgeIt& operator++() { return *this; }
269      };
270
271      /// Iterator class for the incident edges of a node.
272
273      /// This iterator goes trough the incident undirected edges
274      /// of a certain node of a graph.
275      /// Its usage is quite simple, for example, you can compute the
276      /// degree (i.e. the number of incident edges) of a node \c n
277      /// in a graph \c g of type \c %Graph as follows.
278      ///
279      ///\code
280      /// int count=0;
281      /// for(Graph::IncEdgeIt e(g, n); e!=INVALID; ++e) ++count;
282      ///\endcode
283      ///
284      /// \warning Loop edges will be iterated twice.
285      class IncEdgeIt : public Edge {
286      public:
287        /// Default constructor
288
289        /// Default constructor.
290        /// \warning It sets the iterator to an undefined value.
291        IncEdgeIt() { }
292        /// Copy constructor.
293
294        /// Copy constructor.
295        ///
296        IncEdgeIt(const IncEdgeIt& e) : Edge(e) { }
297        /// %Invalid constructor \& conversion.
298
299        /// Initializes the iterator to be invalid.
300        /// \sa Invalid for more details.
301        IncEdgeIt(Invalid) { }
302        /// Sets the iterator to the first incident edge.
303
304        /// Sets the iterator to the first incident edge of the given node.
305        ///
306        IncEdgeIt(const Graph&, const Node&) { }
307        /// Sets the iterator to the given edge.
308
309        /// Sets the iterator to the given edge of the given graph.
310        ///
311        IncEdgeIt(const Graph&, const Edge&) { }
312        /// Next incident edge
313
314        /// Assign the iterator to the next incident edge
315        /// of the corresponding node.
316        IncEdgeIt& operator++() { return *this; }
317      };
318
319      /// The arc type of the graph
320
321      /// This class identifies a directed arc of the graph. It also serves
322      /// as a base class of the arc iterators,
323      /// thus they will convert to this type.
324      class Arc {
325      public:
326        /// Default constructor
327
328        /// Default constructor.
329        /// \warning It sets the object to an undefined value.
330        Arc() { }
331        /// Copy constructor.
332
333        /// Copy constructor.
334        ///
335        Arc(const Arc&) { }
336        /// %Invalid constructor \& conversion.
337
338        /// Initializes the object to be invalid.
339        /// \sa Invalid for more details.
340        Arc(Invalid) { }
341        /// Equality operator
342
343        /// Equality operator.
344        ///
345        /// Two iterators are equal if and only if they point to the
346        /// same object or both are \c INVALID.
347        bool operator==(Arc) const { return true; }
348        /// Inequality operator
349
350        /// Inequality operator.
351        bool operator!=(Arc) const { return true; }
352
353        /// Artificial ordering operator.
354
355        /// Artificial ordering operator.
356        ///
357        /// \note This operator only has to define some strict ordering of
358        /// the arcs; this order has nothing to do with the iteration
359        /// ordering of the arcs.
360        bool operator<(Arc) const { return false; }
361
362        /// Converison to \c Edge
363       
364        /// Converison to \c Edge.
365        ///
366        operator Edge() const { return Edge(); }
367      };
368
369      /// Iterator class for the arcs.
370
371      /// This iterator goes through each directed arc of the graph.
372      /// Its usage is quite simple, for example, you can count the number
373      /// of arcs in a graph \c g of type \c %Graph as follows:
374      ///\code
375      /// int count=0;
376      /// for(Graph::ArcIt a(g); a!=INVALID; ++a) ++count;
377      ///\endcode
378      class ArcIt : public Arc {
379      public:
380        /// Default constructor
381
382        /// Default constructor.
383        /// \warning It sets the iterator to an undefined value.
384        ArcIt() { }
385        /// Copy constructor.
386
387        /// Copy constructor.
388        ///
389        ArcIt(const ArcIt& e) : Arc(e) { }
390        /// %Invalid constructor \& conversion.
391
392        /// Initializes the iterator to be invalid.
393        /// \sa Invalid for more details.
394        ArcIt(Invalid) { }
395        /// Sets the iterator to the first arc.
396
397        /// Sets the iterator to the first arc of the given graph.
398        ///
399        explicit ArcIt(const Graph &g) { ignore_unused_variable_warning(g); }
400        /// Sets the iterator to the given arc.
401
402        /// Sets the iterator to the given arc of the given graph.
403        ///
404        ArcIt(const Graph&, const Arc&) { }
405        /// Next arc
406
407        /// Assign the iterator to the next arc.
408        ///
409        ArcIt& operator++() { return *this; }
410      };
411
412      /// Iterator class for the outgoing arcs of a node.
413
414      /// This iterator goes trough the \e outgoing directed arcs of a
415      /// certain node of a graph.
416      /// Its usage is quite simple, for example, you can count the number
417      /// of outgoing arcs of a node \c n
418      /// in a graph \c g of type \c %Graph as follows.
419      ///\code
420      /// int count=0;
421      /// for (Digraph::OutArcIt a(g, n); a!=INVALID; ++a) ++count;
422      ///\endcode
423      class OutArcIt : public Arc {
424      public:
425        /// Default constructor
426
427        /// Default constructor.
428        /// \warning It sets the iterator to an undefined value.
429        OutArcIt() { }
430        /// Copy constructor.
431
432        /// Copy constructor.
433        ///
434        OutArcIt(const OutArcIt& e) : Arc(e) { }
435        /// %Invalid constructor \& conversion.
436
437        /// Initializes the iterator to be invalid.
438        /// \sa Invalid for more details.
439        OutArcIt(Invalid) { }
440        /// Sets the iterator to the first outgoing arc.
441
442        /// Sets the iterator to the first outgoing arc of the given node.
443        ///
444        OutArcIt(const Graph& n, const Node& g) {
445          ignore_unused_variable_warning(n);
446          ignore_unused_variable_warning(g);
447        }
448        /// Sets the iterator to the given arc.
449
450        /// Sets the iterator to the given arc of the given graph.
451        ///
452        OutArcIt(const Graph&, const Arc&) { }
453        /// Next outgoing arc
454
455        /// Assign the iterator to the next
456        /// outgoing arc of the corresponding node.
457        OutArcIt& operator++() { return *this; }
458      };
459
460      /// Iterator class for the incoming arcs of a node.
461
462      /// This iterator goes trough the \e incoming directed arcs of a
463      /// certain node of a graph.
464      /// Its usage is quite simple, for example, you can count the number
465      /// of incoming arcs of a node \c n
466      /// in a graph \c g of type \c %Graph as follows.
467      ///\code
468      /// int count=0;
469      /// for (Digraph::InArcIt a(g, n); a!=INVALID; ++a) ++count;
470      ///\endcode
471      class InArcIt : public Arc {
472      public:
473        /// Default constructor
474
475        /// Default constructor.
476        /// \warning It sets the iterator to an undefined value.
477        InArcIt() { }
478        /// Copy constructor.
479
480        /// Copy constructor.
481        ///
482        InArcIt(const InArcIt& e) : Arc(e) { }
483        /// %Invalid constructor \& conversion.
484
485        /// Initializes the iterator to be invalid.
486        /// \sa Invalid for more details.
487        InArcIt(Invalid) { }
488        /// Sets the iterator to the first incoming arc.
489
490        /// Sets the iterator to the first incoming arc of the given node.
491        ///
492        InArcIt(const Graph& g, const Node& n) {
493          ignore_unused_variable_warning(n);
494          ignore_unused_variable_warning(g);
495        }
496        /// Sets the iterator to the given arc.
497
498        /// Sets the iterator to the given arc of the given graph.
499        ///
500        InArcIt(const Graph&, const Arc&) { }
501        /// Next incoming arc
502
503        /// Assign the iterator to the next
504        /// incoming arc of the corresponding node.
505        InArcIt& operator++() { return *this; }
506      };
507
508      /// \brief Standard graph map type for the nodes.
509      ///
510      /// Standard graph map type for the nodes.
511      /// It conforms to the ReferenceMap concept.
512      template<class T>
513      class NodeMap : public ReferenceMap<Node, T, T&, const T&>
514      {
515      public:
516
517        /// Constructor
518        explicit NodeMap(const Graph&) { }
519        /// Constructor with given initial value
520        NodeMap(const Graph&, T) { }
521
522      private:
523        ///Copy constructor
524        NodeMap(const NodeMap& nm) :
525          ReferenceMap<Node, T, T&, const T&>(nm) { }
526        ///Assignment operator
527        template <typename CMap>
528        NodeMap& operator=(const CMap&) {
529          checkConcept<ReadMap<Node, T>, CMap>();
530          return *this;
531        }
532      };
533
534      /// \brief Standard graph map type for the arcs.
535      ///
536      /// Standard graph map type for the arcs.
537      /// It conforms to the ReferenceMap concept.
538      template<class T>
539      class ArcMap : public ReferenceMap<Arc, T, T&, const T&>
540      {
541      public:
542
543        /// Constructor
544        explicit ArcMap(const Graph&) { }
545        /// Constructor with given initial value
546        ArcMap(const Graph&, T) { }
547
548      private:
549        ///Copy constructor
550        ArcMap(const ArcMap& em) :
551          ReferenceMap<Arc, T, T&, const T&>(em) { }
552        ///Assignment operator
553        template <typename CMap>
554        ArcMap& operator=(const CMap&) {
555          checkConcept<ReadMap<Arc, T>, CMap>();
556          return *this;
557        }
558      };
559
560      /// \brief Standard graph map type for the edges.
561      ///
562      /// Standard graph map type for the edges.
563      /// It conforms to the ReferenceMap concept.
564      template<class T>
565      class EdgeMap : public ReferenceMap<Edge, T, T&, const T&>
566      {
567      public:
568
569        /// Constructor
570        explicit EdgeMap(const Graph&) { }
571        /// Constructor with given initial value
572        EdgeMap(const Graph&, T) { }
573
574      private:
575        ///Copy constructor
576        EdgeMap(const EdgeMap& em) :
577          ReferenceMap<Edge, T, T&, const T&>(em) {}
578        ///Assignment operator
579        template <typename CMap>
580        EdgeMap& operator=(const CMap&) {
581          checkConcept<ReadMap<Edge, T>, CMap>();
582          return *this;
583        }
584      };
585
586      /// \brief The first node of the edge.
587      ///
588      /// Returns the first node of the given edge.
589      ///
590      /// Edges don't have source and target nodes, however, methods
591      /// u() and v() are used to query the two end-nodes of an edge.
592      /// The orientation of an edge that arises this way is called
593      /// the inherent direction, it is used to define the default
594      /// direction for the corresponding arcs.
595      /// \sa v()
596      /// \sa direction()
597      Node u(Edge) const { return INVALID; }
598
599      /// \brief The second node of the edge.
600      ///
601      /// Returns the second node of the given edge.
602      ///
603      /// Edges don't have source and target nodes, however, methods
604      /// u() and v() are used to query the two end-nodes of an edge.
605      /// The orientation of an edge that arises this way is called
606      /// the inherent direction, it is used to define the default
607      /// direction for the corresponding arcs.
608      /// \sa u()
609      /// \sa direction()
610      Node v(Edge) const { return INVALID; }
611
612      /// \brief The source node of the arc.
613      ///
614      /// Returns the source node of the given arc.
615      Node source(Arc) const { return INVALID; }
616
617      /// \brief The target node of the arc.
618      ///
619      /// Returns the target node of the given arc.
620      Node target(Arc) const { return INVALID; }
621
622      /// \brief The ID of the node.
623      ///
624      /// Returns the ID of the given node.
625      int id(Node) const { return -1; }
626
627      /// \brief The ID of the edge.
628      ///
629      /// Returns the ID of the given edge.
630      int id(Edge) const { return -1; }
631
632      /// \brief The ID of the arc.
633      ///
634      /// Returns the ID of the given arc.
635      int id(Arc) const { return -1; }
636
637      /// \brief The node with the given ID.
638      ///
639      /// Returns the node with the given ID.
640      /// \pre The argument should be a valid node ID in the graph.
641      Node nodeFromId(int) const { return INVALID; }
642
643      /// \brief The edge with the given ID.
644      ///
645      /// Returns the edge with the given ID.
646      /// \pre The argument should be a valid edge ID in the graph.
647      Edge edgeFromId(int) const { return INVALID; }
648
649      /// \brief The arc with the given ID.
650      ///
651      /// Returns the arc with the given ID.
652      /// \pre The argument should be a valid arc ID in the graph.
653      Arc arcFromId(int) const { return INVALID; }
654
655      /// \brief An upper bound on the node IDs.
656      ///
657      /// Returns an upper bound on the node IDs.
658      int maxNodeId() const { return -1; }
659
660      /// \brief An upper bound on the edge IDs.
661      ///
662      /// Returns an upper bound on the edge IDs.
663      int maxEdgeId() const { return -1; }
664
665      /// \brief An upper bound on the arc IDs.
666      ///
667      /// Returns an upper bound on the arc IDs.
668      int maxArcId() const { return -1; }
669
670      /// \brief The direction of the arc.
671      ///
672      /// Returns \c true if the direction of the given arc is the same as
673      /// the inherent orientation of the represented edge.
674      bool direction(Arc) const { return true; }
675
676      /// \brief Direct the edge.
677      ///
678      /// Direct the given edge. The returned arc
679      /// represents the given edge and its direction comes
680      /// from the bool parameter. If it is \c true, then the direction
681      /// of the arc is the same as the inherent orientation of the edge.
682      Arc direct(Edge, bool) const {
683        return INVALID;
684      }
685
686      /// \brief Direct the edge.
687      ///
688      /// Direct the given edge. The returned arc represents the given
689      /// edge and its source node is the given node.
690      Arc direct(Edge, Node) const {
691        return INVALID;
692      }
693
694      /// \brief The oppositely directed arc.
695      ///
696      /// Returns the oppositely directed arc representing the same edge.
697      Arc oppositeArc(Arc) const { return INVALID; }
698
699      /// \brief The opposite node on the edge.
700      ///
701      /// Returns the opposite node on the given edge.
702      Node oppositeNode(Node, Edge) const { return INVALID; }
703
704      void first(Node&) const {}
705      void next(Node&) const {}
706
707      void first(Edge&) const {}
708      void next(Edge&) const {}
709
710      void first(Arc&) const {}
711      void next(Arc&) const {}
712
713      void firstOut(Arc&, Node) const {}
714      void nextOut(Arc&) const {}
715
716      void firstIn(Arc&, Node) const {}
717      void nextIn(Arc&) const {}
718
719      void firstInc(Edge &, bool &, const Node &) const {}
720      void nextInc(Edge &, bool &) const {}
721
722      // The second parameter is dummy.
723      Node fromId(int, Node) const { return INVALID; }
724      // The second parameter is dummy.
725      Edge fromId(int, Edge) const { return INVALID; }
726      // The second parameter is dummy.
727      Arc fromId(int, Arc) const { return INVALID; }
728
729      // Dummy parameter.
730      int maxId(Node) const { return -1; }
731      // Dummy parameter.
732      int maxId(Edge) const { return -1; }
733      // Dummy parameter.
734      int maxId(Arc) const { return -1; }
735
736      /// \brief The base node of the iterator.
737      ///
738      /// Returns the base node of the given incident edge iterator.
739      Node baseNode(IncEdgeIt) const { return INVALID; }
740
741      /// \brief The running node of the iterator.
742      ///
743      /// Returns the running node of the given incident edge iterator.
744      Node runningNode(IncEdgeIt) const { return INVALID; }
745
746      /// \brief The base node of the iterator.
747      ///
748      /// Returns the base node of the given outgoing arc iterator
749      /// (i.e. the source node of the corresponding arc).
750      Node baseNode(OutArcIt) const { return INVALID; }
751
752      /// \brief The running node of the iterator.
753      ///
754      /// Returns the running node of the given outgoing arc iterator
755      /// (i.e. the target node of the corresponding arc).
756      Node runningNode(OutArcIt) const { return INVALID; }
757
758      /// \brief The base node of the iterator.
759      ///
760      /// Returns the base node of the given incomming arc iterator
761      /// (i.e. the target node of the corresponding arc).
762      Node baseNode(InArcIt) const { return INVALID; }
763
764      /// \brief The running node of the iterator.
765      ///
766      /// Returns the running node of the given incomming arc iterator
767      /// (i.e. the source node of the corresponding arc).
768      Node runningNode(InArcIt) const { return INVALID; }
769
770      template <typename _Graph>
771      struct Constraints {
772        void constraints() {
773          checkConcept<BaseGraphComponent, _Graph>();
774          checkConcept<IterableGraphComponent<>, _Graph>();
775          checkConcept<IDableGraphComponent<>, _Graph>();
776          checkConcept<MappableGraphComponent<>, _Graph>();
777        }
778      };
779
780    };
781
782  }
783
784}
785
786#endif
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