COIN-OR::LEMON - Graph Library

source: lemon/lemon/concepts/graph.h @ 212:1ae84dea7d09

Last change on this file since 212:1ae84dea7d09 was 209:765619b7cbb2, checked in by Alpar Juttner <alpar@…>, 12 years ago

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[209]1/* -*- mode: C++; indent-tabs-mode: nil; -*-
[57]2 *
[209]3 * This file is a part of LEMON, a generic C++ optimization library.
[57]4 *
[107]5 * Copyright (C) 2003-2008
[57]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_CONCEPT_GRAPH_H
24#define LEMON_CONCEPT_GRAPH_H
25
26#include <lemon/concepts/graph_components.h>
27#include <lemon/concepts/graph.h>
28#include <lemon/bits/utility.h>
29
30namespace lemon {
31  namespace concepts {
32
33    /// \ingroup graph_concepts
34    ///
35    /// \brief Class describing the concept of Undirected Graphs.
36    ///
37    /// This class describes the common interface of all Undirected
38    /// Graphs.
39    ///
40    /// As all concept describing classes it provides only interface
41    /// without any sensible implementation. So any algorithm for
42    /// undirected graph should compile with this class, but it will not
43    /// run properly, of course.
44    ///
45    /// The LEMON undirected graphs also fulfill the concept of
46    /// directed graphs (\ref lemon::concepts::Digraph "Digraph
47    /// Concept"). Each edges can be seen as two opposite
48    /// directed arc and consequently the undirected graph can be
49    /// seen as the direceted graph of these directed arcs. The
50    /// Graph has the Edge inner class for the edges and
51    /// the Arc type for the directed arcs. The Arc type is
52    /// convertible to Edge or inherited from it so from a directed
53    /// arc we can get the represented edge.
54    ///
55    /// In the sense of the LEMON each edge has a default
56    /// direction (it should be in every computer implementation,
57    /// because the order of edge's nodes defines an
58    /// orientation). With the default orientation we can define that
59    /// the directed arc is forward or backward directed. With the \c
60    /// direction() and \c direct() function we can get the direction
61    /// of the directed arc and we can direct an edge.
62    ///
63    /// The EdgeIt is an iterator for the edges. We can use
64    /// the EdgeMap to map values for the edges. The InArcIt and
65    /// OutArcIt iterates on the same edges but with opposite
[78]66    /// direction. The IncEdgeIt iterates also on the same edges
[57]67    /// as the OutArcIt and InArcIt but it is not convertible to Arc just
[209]68    /// to Edge.
[57]69    class Graph {
70    public:
71      /// \brief The undirected graph should be tagged by the
72      /// UndirectedTag.
73      ///
74      /// The undirected graph should be tagged by the UndirectedTag. This
[209]75      /// tag helps the enable_if technics to make compile time
76      /// specializations for undirected graphs.
[57]77      typedef True UndirectedTag;
78
[209]79      /// \brief The base type of node iterators,
[57]80      /// or in other words, the trivial node iterator.
81      ///
82      /// This is the base type of each node iterator,
83      /// thus each kind of node iterator converts to this.
[209]84      /// More precisely each kind of node iterator should be inherited
[57]85      /// from the trivial node iterator.
86      class Node {
87      public:
88        /// Default constructor
89
90        /// @warning The default constructor sets the iterator
91        /// to an undefined value.
92        Node() { }
93        /// Copy constructor.
94
95        /// Copy constructor.
96        ///
97        Node(const Node&) { }
98
99        /// Invalid constructor \& conversion.
100
101        /// This constructor initializes the iterator to be invalid.
102        /// \sa Invalid for more details.
103        Node(Invalid) { }
104        /// Equality operator
105
106        /// Two iterators are equal if and only if they point to the
107        /// same object or both are invalid.
108        bool operator==(Node) const { return true; }
109
110        /// Inequality operator
[209]111
[57]112        /// \sa operator==(Node n)
113        ///
114        bool operator!=(Node) const { return true; }
115
[209]116        /// Artificial ordering operator.
117
118        /// To allow the use of graph descriptors as key type in std::map or
119        /// similar associative container we require this.
120        ///
121        /// \note This operator only have to define some strict ordering of
122        /// the items; this order has nothing to do with the iteration
123        /// ordering of the items.
124        bool operator<(Node) const { return false; }
[57]125
126      };
[209]127
[57]128      /// This iterator goes through each node.
129
130      /// This iterator goes through each node.
131      /// Its usage is quite simple, for example you can count the number
132      /// of nodes in graph \c g of type \c Graph like this:
133      ///\code
134      /// int count=0;
135      /// for (Graph::NodeIt n(g); n!=INVALID; ++n) ++count;
136      ///\endcode
137      class NodeIt : public Node {
138      public:
139        /// Default constructor
140
141        /// @warning The default constructor sets the iterator
142        /// to an undefined value.
143        NodeIt() { }
144        /// Copy constructor.
[209]145
[57]146        /// Copy constructor.
147        ///
148        NodeIt(const NodeIt& n) : Node(n) { }
149        /// Invalid constructor \& conversion.
150
151        /// Initialize the iterator to be invalid.
152        /// \sa Invalid for more details.
153        NodeIt(Invalid) { }
154        /// Sets the iterator to the first node.
155
156        /// Sets the iterator to the first node of \c g.
157        ///
158        NodeIt(const Graph&) { }
159        /// Node -> NodeIt conversion.
160
[209]161        /// Sets the iterator to the node of \c the graph pointed by
162        /// the trivial iterator.
163        /// This feature necessitates that each time we
[57]164        /// iterate the arc-set, the iteration order is the same.
165        NodeIt(const Graph&, const Node&) { }
166        /// Next node.
167
168        /// Assign the iterator to the next node.
169        ///
170        NodeIt& operator++() { return *this; }
171      };
[209]172
173
[57]174      /// The base type of the edge iterators.
175
176      /// The base type of the edge iterators.
177      ///
178      class Edge {
179      public:
180        /// Default constructor
181
182        /// @warning The default constructor sets the iterator
183        /// to an undefined value.
184        Edge() { }
185        /// Copy constructor.
186
187        /// Copy constructor.
188        ///
189        Edge(const Edge&) { }
190        /// Initialize the iterator to be invalid.
191
192        /// Initialize the iterator to be invalid.
193        ///
194        Edge(Invalid) { }
195        /// Equality operator
196
197        /// Two iterators are equal if and only if they point to the
198        /// same object or both are invalid.
199        bool operator==(Edge) const { return true; }
200        /// Inequality operator
201
202        /// \sa operator==(Edge n)
203        ///
204        bool operator!=(Edge) const { return true; }
205
[209]206        /// Artificial ordering operator.
207
208        /// To allow the use of graph descriptors as key type in std::map or
209        /// similar associative container we require this.
210        ///
211        /// \note This operator only have to define some strict ordering of
212        /// the items; this order has nothing to do with the iteration
213        /// ordering of the items.
214        bool operator<(Edge) const { return false; }
[57]215      };
216
217      /// This iterator goes through each edge.
218
219      /// This iterator goes through each edge of a graph.
220      /// Its usage is quite simple, for example you can count the number
221      /// of edges in a graph \c g of type \c Graph as follows:
222      ///\code
223      /// int count=0;
224      /// for(Graph::EdgeIt e(g); e!=INVALID; ++e) ++count;
225      ///\endcode
226      class EdgeIt : public Edge {
227      public:
228        /// Default constructor
229
230        /// @warning The default constructor sets the iterator
231        /// to an undefined value.
232        EdgeIt() { }
233        /// Copy constructor.
234
235        /// Copy constructor.
236        ///
237        EdgeIt(const EdgeIt& e) : Edge(e) { }
238        /// Initialize the iterator to be invalid.
239
240        /// Initialize the iterator to be invalid.
241        ///
242        EdgeIt(Invalid) { }
243        /// This constructor sets the iterator to the first edge.
[209]244
[57]245        /// This constructor sets the iterator to the first edge.
246        EdgeIt(const Graph&) { }
247        /// Edge -> EdgeIt conversion
248
249        /// Sets the iterator to the value of the trivial iterator.
250        /// This feature necessitates that each time we
[209]251        /// iterate the edge-set, the iteration order is the
252        /// same.
253        EdgeIt(const Graph&, const Edge&) { }
[57]254        /// Next edge
[209]255
[57]256        /// Assign the iterator to the next edge.
257        EdgeIt& operator++() { return *this; }
258      };
259
[209]260      /// \brief This iterator goes trough the incident undirected
[57]261      /// arcs of a node.
262      ///
263      /// This iterator goes trough the incident edges
[209]264      /// of a certain node of a graph. You should assume that the
[57]265      /// loop arcs will be iterated twice.
[209]266      ///
[57]267      /// Its usage is quite simple, for example you can compute the
268      /// degree (i.e. count the number of incident arcs of a node \c n
[209]269      /// in graph \c g of type \c Graph as follows.
[57]270      ///
271      ///\code
272      /// int count=0;
[78]273      /// for(Graph::IncEdgeIt e(g, n); e!=INVALID; ++e) ++count;
[57]274      ///\endcode
[78]275      class IncEdgeIt : public Edge {
[57]276      public:
277        /// Default constructor
278
279        /// @warning The default constructor sets the iterator
280        /// to an undefined value.
[78]281        IncEdgeIt() { }
[57]282        /// Copy constructor.
283
284        /// Copy constructor.
285        ///
[78]286        IncEdgeIt(const IncEdgeIt& e) : Edge(e) { }
[57]287        /// Initialize the iterator to be invalid.
288
289        /// Initialize the iterator to be invalid.
290        ///
[78]291        IncEdgeIt(Invalid) { }
[57]292        /// This constructor sets the iterator to first incident arc.
[209]293
[57]294        /// This constructor set the iterator to the first incident arc of
295        /// the node.
[78]296        IncEdgeIt(const Graph&, const Node&) { }
297        /// Edge -> IncEdgeIt conversion
[57]298
299        /// Sets the iterator to the value of the trivial iterator \c e.
[209]300        /// This feature necessitates that each time we
[57]301        /// iterate the arc-set, the iteration order is the same.
[78]302        IncEdgeIt(const Graph&, const Edge&) { }
[57]303        /// Next incident arc
304
305        /// Assign the iterator to the next incident arc
[209]306        /// of the corresponding node.
[78]307        IncEdgeIt& operator++() { return *this; }
[57]308      };
309
310      /// The directed arc type.
311
312      /// The directed arc type. It can be converted to the
313      /// edge or it should be inherited from the undirected
314      /// arc.
315      class Arc : public Edge {
316      public:
317        /// Default constructor
318
319        /// @warning The default constructor sets the iterator
320        /// to an undefined value.
321        Arc() { }
322        /// Copy constructor.
323
324        /// Copy constructor.
325        ///
326        Arc(const Arc& e) : Edge(e) { }
327        /// Initialize the iterator to be invalid.
328
329        /// Initialize the iterator to be invalid.
330        ///
331        Arc(Invalid) { }
332        /// Equality operator
333
334        /// Two iterators are equal if and only if they point to the
335        /// same object or both are invalid.
336        bool operator==(Arc) const { return true; }
337        /// Inequality operator
338
339        /// \sa operator==(Arc n)
340        ///
341        bool operator!=(Arc) const { return true; }
342
[209]343        /// Artificial ordering operator.
344
345        /// To allow the use of graph descriptors as key type in std::map or
346        /// similar associative container we require this.
347        ///
348        /// \note This operator only have to define some strict ordering of
349        /// the items; this order has nothing to do with the iteration
350        /// ordering of the items.
351        bool operator<(Arc) const { return false; }
352
353      };
[57]354      /// This iterator goes through each directed arc.
355
356      /// This iterator goes through each arc of a graph.
357      /// Its usage is quite simple, for example you can count the number
358      /// of arcs in a graph \c g of type \c Graph as follows:
359      ///\code
360      /// int count=0;
361      /// for(Graph::ArcIt e(g); e!=INVALID; ++e) ++count;
362      ///\endcode
363      class ArcIt : public Arc {
364      public:
365        /// Default constructor
366
367        /// @warning The default constructor sets the iterator
368        /// to an undefined value.
369        ArcIt() { }
370        /// Copy constructor.
371
372        /// Copy constructor.
373        ///
374        ArcIt(const ArcIt& e) : Arc(e) { }
375        /// Initialize the iterator to be invalid.
376
377        /// Initialize the iterator to be invalid.
378        ///
379        ArcIt(Invalid) { }
380        /// This constructor sets the iterator to the first arc.
[209]381
[57]382        /// This constructor sets the iterator to the first arc of \c g.
383        ///@param g the graph
384        ArcIt(const Graph &g) { ignore_unused_variable_warning(g); }
385        /// Arc -> ArcIt conversion
386
387        /// Sets the iterator to the value of the trivial iterator \c e.
[209]388        /// This feature necessitates that each time we
[57]389        /// iterate the arc-set, the iteration order is the same.
[209]390        ArcIt(const Graph&, const Arc&) { }
[57]391        ///Next arc
[209]392
[57]393        /// Assign the iterator to the next arc.
394        ArcIt& operator++() { return *this; }
395      };
[209]396
[57]397      /// This iterator goes trough the outgoing directed arcs of a node.
398
399      /// This iterator goes trough the \e outgoing arcs of a certain node
400      /// of a graph.
401      /// Its usage is quite simple, for example you can count the number
402      /// of outgoing arcs of a node \c n
403      /// in graph \c g of type \c Graph as follows.
404      ///\code
405      /// int count=0;
406      /// for (Graph::OutArcIt e(g, n); e!=INVALID; ++e) ++count;
407      ///\endcode
[209]408
[57]409      class OutArcIt : public Arc {
410      public:
411        /// Default constructor
412
413        /// @warning The default constructor sets the iterator
414        /// to an undefined value.
415        OutArcIt() { }
416        /// Copy constructor.
417
418        /// Copy constructor.
419        ///
420        OutArcIt(const OutArcIt& e) : Arc(e) { }
421        /// Initialize the iterator to be invalid.
422
423        /// Initialize the iterator to be invalid.
424        ///
425        OutArcIt(Invalid) { }
426        /// This constructor sets the iterator to the first outgoing arc.
[209]427
[57]428        /// This constructor sets the iterator to the first outgoing arc of
429        /// the node.
430        ///@param n the node
431        ///@param g the graph
432        OutArcIt(const Graph& n, const Node& g) {
[209]433          ignore_unused_variable_warning(n);
434          ignore_unused_variable_warning(g);
435        }
[57]436        /// Arc -> OutArcIt conversion
437
438        /// Sets the iterator to the value of the trivial iterator.
[209]439        /// This feature necessitates that each time we
[57]440        /// iterate the arc-set, the iteration order is the same.
441        OutArcIt(const Graph&, const Arc&) { }
442        ///Next outgoing arc
[209]443
444        /// Assign the iterator to the next
[57]445        /// outgoing arc of the corresponding node.
446        OutArcIt& operator++() { return *this; }
447      };
448
449      /// This iterator goes trough the incoming directed arcs of a node.
450
451      /// This iterator goes trough the \e incoming arcs of a certain node
452      /// of a graph.
453      /// Its usage is quite simple, for example you can count the number
454      /// of outgoing arcs of a node \c n
455      /// in graph \c g of type \c Graph as follows.
456      ///\code
457      /// int count=0;
458      /// for(Graph::InArcIt e(g, n); e!=INVALID; ++e) ++count;
459      ///\endcode
460
461      class InArcIt : public Arc {
462      public:
463        /// Default constructor
464
465        /// @warning The default constructor sets the iterator
466        /// to an undefined value.
467        InArcIt() { }
468        /// Copy constructor.
469
470        /// Copy constructor.
471        ///
472        InArcIt(const InArcIt& e) : Arc(e) { }
473        /// Initialize the iterator to be invalid.
474
475        /// Initialize the iterator to be invalid.
476        ///
477        InArcIt(Invalid) { }
478        /// This constructor sets the iterator to first incoming arc.
[209]479
[57]480        /// This constructor set the iterator to the first incoming arc of
481        /// the node.
482        ///@param n the node
483        ///@param g the graph
[209]484        InArcIt(const Graph& g, const Node& n) {
485          ignore_unused_variable_warning(n);
486          ignore_unused_variable_warning(g);
487        }
[57]488        /// Arc -> InArcIt conversion
489
490        /// Sets the iterator to the value of the trivial iterator \c e.
[209]491        /// This feature necessitates that each time we
[57]492        /// iterate the arc-set, the iteration order is the same.
493        InArcIt(const Graph&, const Arc&) { }
494        /// Next incoming arc
495
496        /// Assign the iterator to the next inarc of the corresponding node.
497        ///
498        InArcIt& operator++() { return *this; }
499      };
500
501      /// \brief Read write map of the nodes to type \c T.
[209]502      ///
[57]503      /// ReadWrite map of the nodes to type \c T.
504      /// \sa Reference
[209]505      template<class T>
[57]506      class NodeMap : public ReadWriteMap< Node, T >
507      {
508      public:
509
510        ///\e
511        NodeMap(const Graph&) { }
512        ///\e
513        NodeMap(const Graph&, T) { }
514
515        ///Copy constructor
516        NodeMap(const NodeMap& nm) : ReadWriteMap< Node, T >(nm) { }
517        ///Assignment operator
518        template <typename CMap>
[209]519        NodeMap& operator=(const CMap&) {
[57]520          checkConcept<ReadMap<Node, T>, CMap>();
[209]521          return *this;
[57]522        }
523      };
524
525      /// \brief Read write map of the directed arcs to type \c T.
526      ///
527      /// Reference map of the directed arcs to type \c T.
528      /// \sa Reference
[209]529      template<class T>
[57]530      class ArcMap : public ReadWriteMap<Arc,T>
531      {
532      public:
533
534        ///\e
535        ArcMap(const Graph&) { }
536        ///\e
537        ArcMap(const Graph&, T) { }
538        ///Copy constructor
539        ArcMap(const ArcMap& em) : ReadWriteMap<Arc,T>(em) { }
540        ///Assignment operator
541        template <typename CMap>
[209]542        ArcMap& operator=(const CMap&) {
[57]543          checkConcept<ReadMap<Arc, T>, CMap>();
[209]544          return *this;
[57]545        }
546      };
547
548      /// Read write map of the edges to type \c T.
549
550      /// Reference map of the arcs to type \c T.
551      /// \sa Reference
[209]552      template<class T>
[57]553      class EdgeMap : public ReadWriteMap<Edge,T>
554      {
555      public:
556
557        ///\e
558        EdgeMap(const Graph&) { }
559        ///\e
560        EdgeMap(const Graph&, T) { }
561        ///Copy constructor
562        EdgeMap(const EdgeMap& em) : ReadWriteMap<Edge,T>(em) {}
563        ///Assignment operator
564        template <typename CMap>
[209]565        EdgeMap& operator=(const CMap&) {
[57]566          checkConcept<ReadMap<Edge, T>, CMap>();
[209]567          return *this;
[57]568        }
569      };
570
571      /// \brief Direct the given edge.
572      ///
573      /// Direct the given edge. The returned arc source
574      /// will be the given node.
575      Arc direct(const Edge&, const Node&) const {
[209]576        return INVALID;
[57]577      }
578
579      /// \brief Direct the given edge.
580      ///
581      /// Direct the given edge. The returned arc
582      /// represents the given edge and the direction comes
583      /// from the bool parameter. The source of the edge and
584      /// the directed arc is the same when the given bool is true.
585      Arc direct(const Edge&, bool) const {
[209]586        return INVALID;
[57]587      }
588
589      /// \brief Returns true if the arc has default orientation.
590      ///
591      /// Returns whether the given directed arc is same orientation as
592      /// the corresponding edge's default orientation.
593      bool direction(Arc) const { return true; }
594
595      /// \brief Returns the opposite directed arc.
596      ///
597      /// Returns the opposite directed arc.
598      Arc oppositeArc(Arc) const { return INVALID; }
599
600      /// \brief Opposite node on an arc
601      ///
602      /// \return the opposite of the given Node on the given Edge
603      Node oppositeNode(Node, Edge) const { return INVALID; }
604
605      /// \brief First node of the edge.
606      ///
607      /// \return the first node of the given Edge.
608      ///
609      /// Naturally edges don't have direction and thus
610      /// don't have source and target node. But we use these two methods
611      /// to query the two nodes of the arc. The direction of the arc
612      /// which arises this way is called the inherent direction of the
613      /// edge, and is used to define the "default" direction
614      /// of the directed versions of the arcs.
615      /// \sa direction
616      Node u(Edge) const { return INVALID; }
617
618      /// \brief Second node of the edge.
619      Node v(Edge) const { return INVALID; }
620
621      /// \brief Source node of the directed arc.
622      Node source(Arc) const { return INVALID; }
623
624      /// \brief Target node of the directed arc.
625      Node target(Arc) const { return INVALID; }
626
[61]627      /// \brief Returns the id of the node.
[209]628      int id(Node) const { return -1; }
[61]629
630      /// \brief Returns the id of the edge.
[209]631      int id(Edge) const { return -1; }
[61]632
633      /// \brief Returns the id of the arc.
[209]634      int id(Arc) const { return -1; }
[61]635
636      /// \brief Returns the node with the given id.
637      ///
638      /// \pre The argument should be a valid node id in the graph.
[209]639      Node nodeFromId(int) const { return INVALID; }
[61]640
641      /// \brief Returns the edge with the given id.
642      ///
643      /// \pre The argument should be a valid edge id in the graph.
[209]644      Edge edgeFromId(int) const { return INVALID; }
[61]645
646      /// \brief Returns the arc with the given id.
647      ///
648      /// \pre The argument should be a valid arc id in the graph.
[209]649      Arc arcFromId(int) const { return INVALID; }
[61]650
651      /// \brief Returns an upper bound on the node IDs.
[209]652      int maxNodeId() const { return -1; }
[61]653
654      /// \brief Returns an upper bound on the edge IDs.
[209]655      int maxEdgeId() const { return -1; }
[61]656
657      /// \brief Returns an upper bound on the arc IDs.
[209]658      int maxArcId() const { return -1; }
[61]659
[57]660      void first(Node&) const {}
661      void next(Node&) const {}
662
663      void first(Edge&) const {}
664      void next(Edge&) const {}
665
666      void first(Arc&) const {}
667      void next(Arc&) const {}
668
669      void firstOut(Arc&, Node) const {}
670      void nextOut(Arc&) const {}
671
672      void firstIn(Arc&, Node) const {}
673      void nextIn(Arc&) const {}
674
675      void firstInc(Edge &, bool &, const Node &) const {}
676      void nextInc(Edge &, bool &) const {}
677
[61]678      // The second parameter is dummy.
679      Node fromId(int, Node) const { return INVALID; }
680      // The second parameter is dummy.
681      Edge fromId(int, Edge) const { return INVALID; }
682      // The second parameter is dummy.
683      Arc fromId(int, Arc) const { return INVALID; }
684
685      // Dummy parameter.
[209]686      int maxId(Node) const { return -1; }
[61]687      // Dummy parameter.
[209]688      int maxId(Edge) const { return -1; }
[61]689      // Dummy parameter.
[209]690      int maxId(Arc) const { return -1; }
[61]691
[57]692      /// \brief Base node of the iterator
693      ///
694      /// Returns the base node (the source in this case) of the iterator
695      Node baseNode(OutArcIt e) const {
[209]696        return source(e);
[57]697      }
698      /// \brief Running node of the iterator
699      ///
700      /// Returns the running node (the target in this case) of the
701      /// iterator
702      Node runningNode(OutArcIt e) const {
[209]703        return target(e);
[57]704      }
705
706      /// \brief Base node of the iterator
707      ///
708      /// Returns the base node (the target in this case) of the iterator
709      Node baseNode(InArcIt e) const {
[209]710        return target(e);
[57]711      }
712      /// \brief Running node of the iterator
713      ///
714      /// Returns the running node (the source in this case) of the
715      /// iterator
716      Node runningNode(InArcIt e) const {
[209]717        return source(e);
[57]718      }
719
720      /// \brief Base node of the iterator
721      ///
722      /// Returns the base node of the iterator
[78]723      Node baseNode(IncEdgeIt) const {
[209]724        return INVALID;
[57]725      }
[209]726
[57]727      /// \brief Running node of the iterator
728      ///
729      /// Returns the running node of the iterator
[78]730      Node runningNode(IncEdgeIt) const {
[209]731        return INVALID;
[57]732      }
733
[125]734      template <typename _Graph>
[57]735      struct Constraints {
[209]736        void constraints() {
737          checkConcept<IterableGraphComponent<>, _Graph>();
738          checkConcept<IDableGraphComponent<>, _Graph>();
739          checkConcept<MappableGraphComponent<>, _Graph>();
740        }
[57]741      };
742
743    };
744
745  }
746
747}
748
749#endif
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