COIN-OR::LEMON - Graph Library

source: lemon/lemon/concepts/graph.h

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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) 2003-2013
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 GraphCopy instead.
76      Graph(const Graph&) {}
77      /// \brief Assignment of a graph to another one is \e not allowed.
78      /// Use GraphCopy 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) {
400          ::lemon::ignore_unused_variable_warning(g);
401        }
402        /// Sets the iterator to the given arc.
403
404        /// Sets the iterator to the given arc of the given graph.
405        ///
406        ArcIt(const Graph&, const Arc&) { }
407        /// Next arc
408
409        /// Assign the iterator to the next arc.
410        ///
411        ArcIt& operator++() { return *this; }
412      };
413
414      /// Iterator class for the outgoing arcs of a node.
415
416      /// This iterator goes trough the \e outgoing directed arcs of a
417      /// certain node of a graph.
418      /// Its usage is quite simple, for example, you can count the number
419      /// of outgoing arcs of a node \c n
420      /// in a graph \c g of type \c %Graph as follows.
421      ///\code
422      /// int count=0;
423      /// for (Digraph::OutArcIt a(g, n); a!=INVALID; ++a) ++count;
424      ///\endcode
425      class OutArcIt : public Arc {
426      public:
427        /// Default constructor
428
429        /// Default constructor.
430        /// \warning It sets the iterator to an undefined value.
431        OutArcIt() { }
432        /// Copy constructor.
433
434        /// Copy constructor.
435        ///
436        OutArcIt(const OutArcIt& e) : Arc(e) { }
437        /// %Invalid constructor \& conversion.
438
439        /// Initializes the iterator to be invalid.
440        /// \sa Invalid for more details.
441        OutArcIt(Invalid) { }
442        /// Sets the iterator to the first outgoing arc.
443
444        /// Sets the iterator to the first outgoing arc of the given node.
445        ///
446        OutArcIt(const Graph& n, const Node& g) {
447          ::lemon::ignore_unused_variable_warning(n);
448          ::lemon::ignore_unused_variable_warning(g);
449        }
450        /// Sets the iterator to the given arc.
451
452        /// Sets the iterator to the given arc of the given graph.
453        ///
454        OutArcIt(const Graph&, const Arc&) { }
455        /// Next outgoing arc
456
457        /// Assign the iterator to the next
458        /// outgoing arc of the corresponding node.
459        OutArcIt& operator++() { return *this; }
460      };
461
462      /// Iterator class for the incoming arcs of a node.
463
464      /// This iterator goes trough the \e incoming directed arcs of a
465      /// certain node of a graph.
466      /// Its usage is quite simple, for example, you can count the number
467      /// of incoming arcs of a node \c n
468      /// in a graph \c g of type \c %Graph as follows.
469      ///\code
470      /// int count=0;
471      /// for (Digraph::InArcIt a(g, n); a!=INVALID; ++a) ++count;
472      ///\endcode
473      class InArcIt : public Arc {
474      public:
475        /// Default constructor
476
477        /// Default constructor.
478        /// \warning It sets the iterator to an undefined value.
479        InArcIt() { }
480        /// Copy constructor.
481
482        /// Copy constructor.
483        ///
484        InArcIt(const InArcIt& e) : Arc(e) { }
485        /// %Invalid constructor \& conversion.
486
487        /// Initializes the iterator to be invalid.
488        /// \sa Invalid for more details.
489        InArcIt(Invalid) { }
490        /// Sets the iterator to the first incoming arc.
491
492        /// Sets the iterator to the first incoming arc of the given node.
493        ///
494        InArcIt(const Graph& g, const Node& n) {
495          ::lemon::ignore_unused_variable_warning(n);
496          ::lemon::ignore_unused_variable_warning(g);
497        }
498        /// Sets the iterator to the given arc.
499
500        /// Sets the iterator to the given arc of the given graph.
501        ///
502        InArcIt(const Graph&, const Arc&) { }
503        /// Next incoming arc
504
505        /// Assign the iterator to the next
506        /// incoming arc of the corresponding node.
507        InArcIt& operator++() { return *this; }
508      };
509
510      /// \brief Standard graph map type for the nodes.
511      ///
512      /// Standard graph map type for the nodes.
513      /// It conforms to the ReferenceMap concept.
514      template<class T>
515      class NodeMap : public ReferenceMap<Node, T, T&, const T&>
516      {
517      public:
518
519        /// Constructor
520        explicit NodeMap(const Graph&) { }
521        /// Constructor with given initial value
522        NodeMap(const Graph&, T) { }
523
524      private:
525        ///Copy constructor
526        NodeMap(const NodeMap& nm) :
527          ReferenceMap<Node, T, T&, const T&>(nm) { }
528        ///Assignment operator
529        template <typename CMap>
530        NodeMap& operator=(const CMap&) {
531          checkConcept<ReadMap<Node, T>, CMap>();
532          return *this;
533        }
534      };
535
536      /// \brief Standard graph map type for the arcs.
537      ///
538      /// Standard graph map type for the arcs.
539      /// It conforms to the ReferenceMap concept.
540      template<class T>
541      class ArcMap : public ReferenceMap<Arc, T, T&, const T&>
542      {
543      public:
544
545        /// Constructor
546        explicit ArcMap(const Graph&) { }
547        /// Constructor with given initial value
548        ArcMap(const Graph&, T) { }
549
550      private:
551        ///Copy constructor
552        ArcMap(const ArcMap& em) :
553          ReferenceMap<Arc, T, T&, const T&>(em) { }
554        ///Assignment operator
555        template <typename CMap>
556        ArcMap& operator=(const CMap&) {
557          checkConcept<ReadMap<Arc, T>, CMap>();
558          return *this;
559        }
560      };
561
562      /// \brief Standard graph map type for the edges.
563      ///
564      /// Standard graph map type for the edges.
565      /// It conforms to the ReferenceMap concept.
566      template<class T>
567      class EdgeMap : public ReferenceMap<Edge, T, T&, const T&>
568      {
569      public:
570
571        /// Constructor
572        explicit EdgeMap(const Graph&) { }
573        /// Constructor with given initial value
574        EdgeMap(const Graph&, T) { }
575
576      private:
577        ///Copy constructor
578        EdgeMap(const EdgeMap& em) :
579          ReferenceMap<Edge, T, T&, const T&>(em) {}
580        ///Assignment operator
581        template <typename CMap>
582        EdgeMap& operator=(const CMap&) {
583          checkConcept<ReadMap<Edge, T>, CMap>();
584          return *this;
585        }
586      };
587
588      /// \brief The first node of the edge.
589      ///
590      /// Returns the first node of the given edge.
591      ///
592      /// Edges don't have source and target nodes, however, methods
593      /// u() and v() are used to query the two end-nodes of an edge.
594      /// The orientation of an edge that arises this way is called
595      /// the inherent direction, it is used to define the default
596      /// direction for the corresponding arcs.
597      /// \sa v()
598      /// \sa direction()
599      Node u(Edge) const { return INVALID; }
600
601      /// \brief The second node of the edge.
602      ///
603      /// Returns the second node of the given edge.
604      ///
605      /// Edges don't have source and target nodes, however, methods
606      /// u() and v() are used to query the two end-nodes of an edge.
607      /// The orientation of an edge that arises this way is called
608      /// the inherent direction, it is used to define the default
609      /// direction for the corresponding arcs.
610      /// \sa u()
611      /// \sa direction()
612      Node v(Edge) const { return INVALID; }
613
614      /// \brief The source node of the arc.
615      ///
616      /// Returns the source node of the given arc.
617      Node source(Arc) const { return INVALID; }
618
619      /// \brief The target node of the arc.
620      ///
621      /// Returns the target node of the given arc.
622      Node target(Arc) const { return INVALID; }
623
624      /// \brief The ID of the node.
625      ///
626      /// Returns the ID of the given node.
627      int id(Node) const { return -1; }
628
629      /// \brief The ID of the edge.
630      ///
631      /// Returns the ID of the given edge.
632      int id(Edge) const { return -1; }
633
634      /// \brief The ID of the arc.
635      ///
636      /// Returns the ID of the given arc.
637      int id(Arc) const { return -1; }
638
639      /// \brief The node with the given ID.
640      ///
641      /// Returns the node with the given ID.
642      /// \pre The argument should be a valid node ID in the graph.
643      Node nodeFromId(int) const { return INVALID; }
644
645      /// \brief The edge with the given ID.
646      ///
647      /// Returns the edge with the given ID.
648      /// \pre The argument should be a valid edge ID in the graph.
649      Edge edgeFromId(int) const { return INVALID; }
650
651      /// \brief The arc with the given ID.
652      ///
653      /// Returns the arc with the given ID.
654      /// \pre The argument should be a valid arc ID in the graph.
655      Arc arcFromId(int) const { return INVALID; }
656
657      /// \brief An upper bound on the node IDs.
658      ///
659      /// Returns an upper bound on the node IDs.
660      int maxNodeId() const { return -1; }
661
662      /// \brief An upper bound on the edge IDs.
663      ///
664      /// Returns an upper bound on the edge IDs.
665      int maxEdgeId() const { return -1; }
666
667      /// \brief An upper bound on the arc IDs.
668      ///
669      /// Returns an upper bound on the arc IDs.
670      int maxArcId() const { return -1; }
671
672      /// \brief The direction of the arc.
673      ///
674      /// Returns \c true if the direction of the given arc is the same as
675      /// the inherent orientation of the represented edge.
676      bool direction(Arc) const { return true; }
677
678      /// \brief Direct the edge.
679      ///
680      /// Direct the given edge. The returned arc
681      /// represents the given edge and its direction comes
682      /// from the bool parameter. If it is \c true, then the direction
683      /// of the arc is the same as the inherent orientation of the edge.
684      Arc direct(Edge, bool) const {
685        return INVALID;
686      }
687
688      /// \brief Direct the edge.
689      ///
690      /// Direct the given edge. The returned arc represents the given
691      /// edge and its source node is the given node.
692      Arc direct(Edge, Node) const {
693        return INVALID;
694      }
695
696      /// \brief The oppositely directed arc.
697      ///
698      /// Returns the oppositely directed arc representing the same edge.
699      Arc oppositeArc(Arc) const { return INVALID; }
700
701      /// \brief The opposite node on the edge.
702      ///
703      /// Returns the opposite node on the given edge.
704      Node oppositeNode(Node, Edge) const { return INVALID; }
705
706      void first(Node&) const {}
707      void next(Node&) const {}
708
709      void first(Edge&) const {}
710      void next(Edge&) const {}
711
712      void first(Arc&) const {}
713      void next(Arc&) const {}
714
715      void firstOut(Arc&, Node) const {}
716      void nextOut(Arc&) const {}
717
718      void firstIn(Arc&, Node) const {}
719      void nextIn(Arc&) const {}
720
721      void firstInc(Edge &, bool &, const Node &) const {}
722      void nextInc(Edge &, bool &) const {}
723
724      // The second parameter is dummy.
725      Node fromId(int, Node) const { return INVALID; }
726      // The second parameter is dummy.
727      Edge fromId(int, Edge) const { return INVALID; }
728      // The second parameter is dummy.
729      Arc fromId(int, Arc) const { return INVALID; }
730
731      // Dummy parameter.
732      int maxId(Node) const { return -1; }
733      // Dummy parameter.
734      int maxId(Edge) const { return -1; }
735      // Dummy parameter.
736      int maxId(Arc) const { return -1; }
737
738      /// \brief The base node of the iterator.
739      ///
740      /// Returns the base node of the given incident edge iterator.
741      Node baseNode(IncEdgeIt) const { return INVALID; }
742
743      /// \brief The running node of the iterator.
744      ///
745      /// Returns the running node of the given incident edge iterator.
746      Node runningNode(IncEdgeIt) const { return INVALID; }
747
748      /// \brief The base node of the iterator.
749      ///
750      /// Returns the base node of the given outgoing arc iterator
751      /// (i.e. the source node of the corresponding arc).
752      Node baseNode(OutArcIt) const { return INVALID; }
753
754      /// \brief The running node of the iterator.
755      ///
756      /// Returns the running node of the given outgoing arc iterator
757      /// (i.e. the target node of the corresponding arc).
758      Node runningNode(OutArcIt) const { return INVALID; }
759
760      /// \brief The base node of the iterator.
761      ///
762      /// Returns the base node of the given incoming arc iterator
763      /// (i.e. the target node of the corresponding arc).
764      Node baseNode(InArcIt) const { return INVALID; }
765
766      /// \brief The running node of the iterator.
767      ///
768      /// Returns the running node of the given incoming arc iterator
769      /// (i.e. the source node of the corresponding arc).
770      Node runningNode(InArcIt) const { return INVALID; }
771
772      template <typename _Graph>
773      struct Constraints {
774        void constraints() {
775          checkConcept<BaseGraphComponent, _Graph>();
776          checkConcept<IterableGraphComponent<>, _Graph>();
777          checkConcept<IDableGraphComponent<>, _Graph>();
778          checkConcept<MappableGraphComponent<>, _Graph>();
779        }
780      };
781
782    };
783
784  }
785
786}
787
788#endif
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