graph_concepts.hpp 19 KB

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  1. //
  2. //=======================================================================
  3. // Copyright 1997, 1998, 1999, 2000 University of Notre Dame.
  4. // Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek
  5. //
  6. // Copyright 2009, Andrew Sutton
  7. //
  8. // Distributed under the Boost Software License, Version 1.0. (See
  9. // accompanying file LICENSE_1_0.txt or copy at
  10. // http://www.boost.org/LICENSE_1_0.txt)
  11. //=======================================================================
  12. //
  13. #ifndef BOOST_GRAPH_CONCEPTS_HPP
  14. #define BOOST_GRAPH_CONCEPTS_HPP
  15. #include <boost/config.hpp>
  16. #include <boost/property_map/property_map.hpp>
  17. #include <boost/graph/graph_traits.hpp>
  18. #include <boost/graph/properties.hpp>
  19. #include <boost/graph/numeric_values.hpp>
  20. #include <boost/graph/buffer_concepts.hpp>
  21. #include <boost/concept_check.hpp>
  22. #include <boost/type_traits/is_same.hpp>
  23. #include <boost/mpl/not.hpp>
  24. #include <boost/static_assert.hpp>
  25. #include <boost/detail/workaround.hpp>
  26. #include <boost/concept/assert.hpp>
  27. #include <boost/concept/detail/concept_def.hpp>
  28. namespace boost
  29. {
  30. // dwa 2003/7/11 -- This clearly shouldn't be necessary, but if
  31. // you want to use vector_as_graph, it is! I'm sure the graph
  32. // library leaves these out all over the place. Probably a
  33. // redesign involving specializing a template with a static
  34. // member function is in order :(
  35. //
  36. // It is needed in order to allow us to write using boost::vertices as
  37. // needed for ADL when using vector_as_graph below.
  38. #if !defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP) \
  39. && !BOOST_WORKAROUND(BOOST_BORLANDC, BOOST_TESTED_AT(0x564))
  40. #define BOOST_VECTOR_AS_GRAPH_GRAPH_ADL_HACK
  41. #endif
  42. #ifdef BOOST_VECTOR_AS_GRAPH_GRAPH_ADL_HACK
  43. template < class T >
  44. typename T::ThereReallyIsNoMemberByThisNameInT vertices(T const&);
  45. #endif
  46. namespace concepts
  47. {
  48. BOOST_concept(MultiPassInputIterator, (T)) { BOOST_CONCEPT_USAGE(
  49. MultiPassInputIterator) { BOOST_CONCEPT_ASSERT((InputIterator< T >));
  50. }
  51. };
  52. BOOST_concept(Graph, (G))
  53. {
  54. typedef typename graph_traits< G >::vertex_descriptor vertex_descriptor;
  55. typedef typename graph_traits< G >::edge_descriptor edge_descriptor;
  56. typedef typename graph_traits< G >::directed_category directed_category;
  57. typedef typename graph_traits< G >::edge_parallel_category
  58. edge_parallel_category;
  59. typedef typename graph_traits< G >::traversal_category traversal_category;
  60. BOOST_CONCEPT_USAGE(Graph)
  61. {
  62. BOOST_CONCEPT_ASSERT((DefaultConstructible< vertex_descriptor >));
  63. BOOST_CONCEPT_ASSERT((EqualityComparable< vertex_descriptor >));
  64. BOOST_CONCEPT_ASSERT((Assignable< vertex_descriptor >));
  65. }
  66. G g;
  67. };
  68. BOOST_concept(IncidenceGraph, (G)) : Graph< G >
  69. {
  70. typedef typename graph_traits< G >::edge_descriptor edge_descriptor;
  71. typedef typename graph_traits< G >::out_edge_iterator out_edge_iterator;
  72. typedef typename graph_traits< G >::degree_size_type degree_size_type;
  73. typedef typename graph_traits< G >::traversal_category traversal_category;
  74. BOOST_STATIC_ASSERT(
  75. (boost::mpl::not_< boost::is_same< out_edge_iterator, void > >::value));
  76. BOOST_STATIC_ASSERT(
  77. (boost::mpl::not_< boost::is_same< degree_size_type, void > >::value));
  78. BOOST_CONCEPT_USAGE(IncidenceGraph)
  79. {
  80. BOOST_CONCEPT_ASSERT((MultiPassInputIterator< out_edge_iterator >));
  81. BOOST_CONCEPT_ASSERT((DefaultConstructible< edge_descriptor >));
  82. BOOST_CONCEPT_ASSERT((EqualityComparable< edge_descriptor >));
  83. BOOST_CONCEPT_ASSERT((Assignable< edge_descriptor >));
  84. BOOST_CONCEPT_ASSERT(
  85. (Convertible< traversal_category, incidence_graph_tag >));
  86. p = out_edges(u, g);
  87. n = out_degree(u, g);
  88. e = *p.first;
  89. u = source(e, g);
  90. v = target(e, g);
  91. const_constraints(g);
  92. }
  93. void const_constraints(const G& cg)
  94. {
  95. p = out_edges(u, cg);
  96. n = out_degree(u, cg);
  97. e = *p.first;
  98. u = source(e, cg);
  99. v = target(e, cg);
  100. }
  101. std::pair< out_edge_iterator, out_edge_iterator > p;
  102. typename graph_traits< G >::vertex_descriptor u, v;
  103. typename graph_traits< G >::edge_descriptor e;
  104. typename graph_traits< G >::degree_size_type n;
  105. G g;
  106. };
  107. BOOST_concept(BidirectionalGraph, (G)) : IncidenceGraph< G >
  108. {
  109. typedef typename graph_traits< G >::in_edge_iterator in_edge_iterator;
  110. typedef typename graph_traits< G >::traversal_category traversal_category;
  111. BOOST_CONCEPT_USAGE(BidirectionalGraph)
  112. {
  113. BOOST_CONCEPT_ASSERT((MultiPassInputIterator< in_edge_iterator >));
  114. BOOST_CONCEPT_ASSERT(
  115. (Convertible< traversal_category, bidirectional_graph_tag >));
  116. BOOST_STATIC_ASSERT((boost::mpl::not_<
  117. boost::is_same< in_edge_iterator, void > >::value));
  118. p = in_edges(v, g);
  119. n = in_degree(v, g);
  120. n = degree(v, g);
  121. e = *p.first;
  122. const_constraints(g);
  123. }
  124. void const_constraints(const G& cg)
  125. {
  126. p = in_edges(v, cg);
  127. n = in_degree(v, cg);
  128. n = degree(v, cg);
  129. e = *p.first;
  130. }
  131. std::pair< in_edge_iterator, in_edge_iterator > p;
  132. typename graph_traits< G >::vertex_descriptor v;
  133. typename graph_traits< G >::edge_descriptor e;
  134. typename graph_traits< G >::degree_size_type n;
  135. G g;
  136. };
  137. BOOST_concept(AdjacencyGraph, (G)) : Graph< G >
  138. {
  139. typedef typename graph_traits< G >::adjacency_iterator adjacency_iterator;
  140. typedef typename graph_traits< G >::traversal_category traversal_category;
  141. BOOST_CONCEPT_USAGE(AdjacencyGraph)
  142. {
  143. BOOST_CONCEPT_ASSERT((MultiPassInputIterator< adjacency_iterator >));
  144. BOOST_CONCEPT_ASSERT(
  145. (Convertible< traversal_category, adjacency_graph_tag >));
  146. BOOST_STATIC_ASSERT((boost::mpl::not_<
  147. boost::is_same< adjacency_iterator, void > >::value));
  148. p = adjacent_vertices(v, g);
  149. v = *p.first;
  150. const_constraints(g);
  151. }
  152. void const_constraints(const G& cg) { p = adjacent_vertices(v, cg); }
  153. std::pair< adjacency_iterator, adjacency_iterator > p;
  154. typename graph_traits< G >::vertex_descriptor v;
  155. G g;
  156. };
  157. BOOST_concept(VertexListGraph, (G)) : Graph< G >
  158. {
  159. typedef typename graph_traits< G >::vertex_iterator vertex_iterator;
  160. typedef typename graph_traits< G >::vertices_size_type vertices_size_type;
  161. typedef typename graph_traits< G >::traversal_category traversal_category;
  162. BOOST_CONCEPT_USAGE(VertexListGraph)
  163. {
  164. BOOST_CONCEPT_ASSERT((MultiPassInputIterator< vertex_iterator >));
  165. BOOST_CONCEPT_ASSERT(
  166. (Convertible< traversal_category, vertex_list_graph_tag >));
  167. BOOST_STATIC_ASSERT((boost::mpl::not_<
  168. boost::is_same< vertex_iterator, void > >::value));
  169. BOOST_STATIC_ASSERT((boost::mpl::not_<
  170. boost::is_same< vertices_size_type, void > >::value));
  171. #ifdef BOOST_VECTOR_AS_GRAPH_GRAPH_ADL_HACK
  172. // dwa 2003/7/11 -- This clearly shouldn't be necessary, but if
  173. // you want to use vector_as_graph, it is! I'm sure the graph
  174. // library leaves these out all over the place. Probably a
  175. // redesign involving specializing a template with a static
  176. // member function is in order :(
  177. using boost::vertices;
  178. #endif
  179. p = vertices(g);
  180. v = *p.first;
  181. const_constraints(g);
  182. }
  183. void const_constraints(const G& cg)
  184. {
  185. #ifdef BOOST_VECTOR_AS_GRAPH_GRAPH_ADL_HACK
  186. // dwa 2003/7/11 -- This clearly shouldn't be necessary, but if
  187. // you want to use vector_as_graph, it is! I'm sure the graph
  188. // library leaves these out all over the place. Probably a
  189. // redesign involving specializing a template with a static
  190. // member function is in order :(
  191. using boost::vertices;
  192. #endif
  193. p = vertices(cg);
  194. v = *p.first;
  195. V = num_vertices(cg);
  196. }
  197. std::pair< vertex_iterator, vertex_iterator > p;
  198. typename graph_traits< G >::vertex_descriptor v;
  199. G g;
  200. vertices_size_type V;
  201. };
  202. BOOST_concept(EdgeListGraph, (G)) : Graph< G >
  203. {
  204. typedef typename graph_traits< G >::edge_descriptor edge_descriptor;
  205. typedef typename graph_traits< G >::edge_iterator edge_iterator;
  206. typedef typename graph_traits< G >::edges_size_type edges_size_type;
  207. typedef typename graph_traits< G >::traversal_category traversal_category;
  208. BOOST_CONCEPT_USAGE(EdgeListGraph)
  209. {
  210. BOOST_CONCEPT_ASSERT((MultiPassInputIterator< edge_iterator >));
  211. BOOST_CONCEPT_ASSERT((DefaultConstructible< edge_descriptor >));
  212. BOOST_CONCEPT_ASSERT((EqualityComparable< edge_descriptor >));
  213. BOOST_CONCEPT_ASSERT((Assignable< edge_descriptor >));
  214. BOOST_CONCEPT_ASSERT(
  215. (Convertible< traversal_category, edge_list_graph_tag >));
  216. BOOST_STATIC_ASSERT(
  217. (boost::mpl::not_< boost::is_same< edge_iterator, void > >::value));
  218. BOOST_STATIC_ASSERT((boost::mpl::not_<
  219. boost::is_same< edges_size_type, void > >::value));
  220. p = edges(g);
  221. e = *p.first;
  222. u = source(e, g);
  223. v = target(e, g);
  224. const_constraints(g);
  225. }
  226. void const_constraints(const G& cg)
  227. {
  228. p = edges(cg);
  229. E = num_edges(cg);
  230. e = *p.first;
  231. u = source(e, cg);
  232. v = target(e, cg);
  233. }
  234. std::pair< edge_iterator, edge_iterator > p;
  235. typename graph_traits< G >::vertex_descriptor u, v;
  236. typename graph_traits< G >::edge_descriptor e;
  237. edges_size_type E;
  238. G g;
  239. };
  240. BOOST_concept(VertexAndEdgeListGraph, (G))
  241. : VertexListGraph< G >, EdgeListGraph< G > {};
  242. // Where to put the requirement for this constructor?
  243. // G g(n_vertices);
  244. // Not in mutable graph, then LEDA graph's can't be models of
  245. // MutableGraph.
  246. BOOST_concept(EdgeMutableGraph, (G))
  247. {
  248. typedef typename graph_traits< G >::edge_descriptor edge_descriptor;
  249. BOOST_CONCEPT_USAGE(EdgeMutableGraph)
  250. {
  251. p = add_edge(u, v, g);
  252. remove_edge(u, v, g);
  253. remove_edge(e, g);
  254. clear_vertex(v, g);
  255. }
  256. G g;
  257. edge_descriptor e;
  258. std::pair< edge_descriptor, bool > p;
  259. typename graph_traits< G >::vertex_descriptor u, v;
  260. };
  261. BOOST_concept(VertexMutableGraph, (G))
  262. {
  263. BOOST_CONCEPT_USAGE(VertexMutableGraph)
  264. {
  265. v = add_vertex(g);
  266. remove_vertex(v, g);
  267. }
  268. G g;
  269. typename graph_traits< G >::vertex_descriptor u, v;
  270. };
  271. BOOST_concept(MutableGraph, (G))
  272. : EdgeMutableGraph< G >, VertexMutableGraph< G > {};
  273. template < class edge_descriptor > struct dummy_edge_predicate
  274. {
  275. bool operator()(const edge_descriptor&) const { return false; }
  276. };
  277. BOOST_concept(MutableIncidenceGraph, (G)) : MutableGraph< G >
  278. {
  279. BOOST_CONCEPT_USAGE(MutableIncidenceGraph)
  280. {
  281. remove_edge(iter, g);
  282. remove_out_edge_if(u, p, g);
  283. }
  284. G g;
  285. typedef typename graph_traits< G >::edge_descriptor edge_descriptor;
  286. dummy_edge_predicate< edge_descriptor > p;
  287. typename boost::graph_traits< G >::vertex_descriptor u;
  288. typename boost::graph_traits< G >::out_edge_iterator iter;
  289. };
  290. BOOST_concept(MutableBidirectionalGraph, (G)) : MutableIncidenceGraph< G >
  291. {
  292. BOOST_CONCEPT_USAGE(MutableBidirectionalGraph)
  293. {
  294. remove_in_edge_if(u, p, g);
  295. }
  296. G g;
  297. typedef typename graph_traits< G >::edge_descriptor edge_descriptor;
  298. dummy_edge_predicate< edge_descriptor > p;
  299. typename boost::graph_traits< G >::vertex_descriptor u;
  300. };
  301. BOOST_concept(MutableEdgeListGraph, (G)) : EdgeMutableGraph< G >
  302. {
  303. BOOST_CONCEPT_USAGE(MutableEdgeListGraph) { remove_edge_if(p, g); }
  304. G g;
  305. typedef typename graph_traits< G >::edge_descriptor edge_descriptor;
  306. dummy_edge_predicate< edge_descriptor > p;
  307. };
  308. BOOST_concept(VertexMutablePropertyGraph, (G)) : VertexMutableGraph< G >
  309. {
  310. BOOST_CONCEPT_USAGE(VertexMutablePropertyGraph) { v = add_vertex(vp, g); }
  311. G g;
  312. typename graph_traits< G >::vertex_descriptor v;
  313. typename vertex_property_type< G >::type vp;
  314. };
  315. BOOST_concept(EdgeMutablePropertyGraph, (G)) : EdgeMutableGraph< G >
  316. {
  317. typedef typename graph_traits< G >::edge_descriptor edge_descriptor;
  318. BOOST_CONCEPT_USAGE(EdgeMutablePropertyGraph) { p = add_edge(u, v, ep, g); }
  319. G g;
  320. std::pair< edge_descriptor, bool > p;
  321. typename graph_traits< G >::vertex_descriptor u, v;
  322. typename edge_property_type< G >::type ep;
  323. };
  324. BOOST_concept(AdjacencyMatrix, (G)) : Graph< G >
  325. {
  326. typedef typename graph_traits< G >::edge_descriptor edge_descriptor;
  327. BOOST_CONCEPT_USAGE(AdjacencyMatrix)
  328. {
  329. p = edge(u, v, g);
  330. const_constraints(g);
  331. }
  332. void const_constraints(const G& cg) { p = edge(u, v, cg); }
  333. typename graph_traits< G >::vertex_descriptor u, v;
  334. std::pair< edge_descriptor, bool > p;
  335. G g;
  336. };
  337. BOOST_concept(ReadablePropertyGraph, (G)(X)(Property)) : Graph< G >
  338. {
  339. typedef typename property_map< G, Property >::const_type const_Map;
  340. BOOST_CONCEPT_USAGE(ReadablePropertyGraph)
  341. {
  342. BOOST_CONCEPT_ASSERT((ReadablePropertyMapConcept< const_Map, X >));
  343. const_constraints(g);
  344. }
  345. void const_constraints(const G& cg)
  346. {
  347. const_Map pmap = get(Property(), cg);
  348. pval = get(Property(), cg, x);
  349. ignore_unused_variable_warning(pmap);
  350. }
  351. G g;
  352. X x;
  353. typename property_traits< const_Map >::value_type pval;
  354. };
  355. BOOST_concept(PropertyGraph, (G)(X)(Property))
  356. : ReadablePropertyGraph< G, X, Property >
  357. {
  358. typedef typename property_map< G, Property >::type Map;
  359. BOOST_CONCEPT_USAGE(PropertyGraph)
  360. {
  361. BOOST_CONCEPT_ASSERT((ReadWritePropertyMapConcept< Map, X >));
  362. Map pmap = get(Property(), g);
  363. pval = get(Property(), g, x);
  364. put(Property(), g, x, pval);
  365. ignore_unused_variable_warning(pmap);
  366. }
  367. G g;
  368. X x;
  369. typename property_traits< Map >::value_type pval;
  370. };
  371. BOOST_concept(LvaluePropertyGraph, (G)(X)(Property))
  372. : ReadablePropertyGraph< G, X, Property >
  373. {
  374. typedef typename property_map< G, Property >::type Map;
  375. typedef typename property_map< G, Property >::const_type const_Map;
  376. BOOST_CONCEPT_USAGE(LvaluePropertyGraph)
  377. {
  378. BOOST_CONCEPT_ASSERT((LvaluePropertyMapConcept< const_Map, X >));
  379. pval = get(Property(), g, x);
  380. put(Property(), g, x, pval);
  381. }
  382. G g;
  383. X x;
  384. typename property_traits< Map >::value_type pval;
  385. };
  386. // The *IndexGraph concepts are "semantic" graph concpepts. These can be
  387. // applied to describe any graph that has an index map that can be accessed
  388. // using the get(*_index, g) method. For example, adjacency lists with
  389. // VertexSet == vecS are implicitly models of this concept.
  390. //
  391. // NOTE: We could require an associated type vertex_index_type, but that
  392. // would mean propagating that type name into graph_traits and all of the
  393. // other graph implementations. Much easier to simply call it unsigned.
  394. BOOST_concept(VertexIndexGraph, (Graph))
  395. {
  396. BOOST_CONCEPT_USAGE(VertexIndexGraph)
  397. {
  398. typedef typename graph_traits< Graph >::vertex_descriptor Vertex;
  399. typedef typename property_map< Graph, vertex_index_t >::type Map;
  400. typedef unsigned Index; // This could be Graph::vertex_index_type
  401. Map m = get(vertex_index, g);
  402. Index x = get(vertex_index, g, Vertex());
  403. ignore_unused_variable_warning(m);
  404. ignore_unused_variable_warning(x);
  405. // This is relaxed
  406. renumber_vertex_indices(g);
  407. const_constraints(g);
  408. }
  409. void const_constraints(const Graph& g_)
  410. {
  411. typedef typename property_map< Graph, vertex_index_t >::const_type Map;
  412. Map m = get(vertex_index, g_);
  413. ignore_unused_variable_warning(m);
  414. }
  415. private:
  416. Graph g;
  417. };
  418. BOOST_concept(EdgeIndexGraph, (Graph))
  419. {
  420. BOOST_CONCEPT_USAGE(EdgeIndexGraph)
  421. {
  422. typedef typename graph_traits< Graph >::edge_descriptor Edge;
  423. typedef typename property_map< Graph, edge_index_t >::type Map;
  424. typedef unsigned Index; // This could be Graph::vertex_index_type
  425. Map m = get(edge_index, g);
  426. Index x = get(edge_index, g, Edge());
  427. ignore_unused_variable_warning(m);
  428. ignore_unused_variable_warning(x);
  429. // This is relaxed
  430. renumber_edge_indices(g);
  431. const_constraints(g);
  432. }
  433. void const_constraints(const Graph& g_)
  434. {
  435. typedef typename property_map< Graph, edge_index_t >::const_type Map;
  436. Map m = get(edge_index, g_);
  437. ignore_unused_variable_warning(m);
  438. }
  439. private:
  440. Graph g;
  441. };
  442. BOOST_concept(ColorValue, (C))
  443. : EqualityComparable< C >, DefaultConstructible< C >
  444. {
  445. BOOST_CONCEPT_USAGE(ColorValue)
  446. {
  447. c = color_traits< C >::white();
  448. c = color_traits< C >::gray();
  449. c = color_traits< C >::black();
  450. }
  451. C c;
  452. };
  453. BOOST_concept(BasicMatrix, (M)(I)(V))
  454. {
  455. BOOST_CONCEPT_USAGE(BasicMatrix)
  456. {
  457. V& elt = A[i][j];
  458. const_constraints(A);
  459. ignore_unused_variable_warning(elt);
  460. }
  461. void const_constraints(const M& cA)
  462. {
  463. const V& elt = cA[i][j];
  464. ignore_unused_variable_warning(elt);
  465. }
  466. M A;
  467. I i, j;
  468. };
  469. // The following concepts describe aspects of numberic values and measure
  470. // functions. We're extending the notion of numeric values to include
  471. // emulation for zero and infinity.
  472. BOOST_concept(NumericValue, (Numeric)) { BOOST_CONCEPT_USAGE(NumericValue) {
  473. BOOST_CONCEPT_ASSERT((DefaultConstructible< Numeric >));
  474. BOOST_CONCEPT_ASSERT((CopyConstructible< Numeric >));
  475. numeric_values< Numeric >::zero();
  476. numeric_values< Numeric >::infinity();
  477. }
  478. }
  479. ;
  480. BOOST_concept(DegreeMeasure, (Measure)(Graph))
  481. {
  482. BOOST_CONCEPT_USAGE(DegreeMeasure)
  483. {
  484. typedef typename Measure::degree_type Degree;
  485. typedef typename Measure::vertex_type Vertex;
  486. Degree d = m(Vertex(), g);
  487. ignore_unused_variable_warning(d);
  488. }
  489. private:
  490. Measure m;
  491. Graph g;
  492. };
  493. BOOST_concept(DistanceMeasure, (Measure)(Graph))
  494. {
  495. BOOST_CONCEPT_USAGE(DistanceMeasure)
  496. {
  497. typedef typename Measure::distance_type Distance;
  498. typedef typename Measure::result_type Result;
  499. Result r = m(Distance(), g);
  500. ignore_unused_variable_warning(r);
  501. }
  502. private:
  503. Measure m;
  504. Graph g;
  505. };
  506. } /* namespace concepts */
  507. using boost::concepts::MultiPassInputIteratorConcept;
  508. // Graph concepts
  509. using boost::concepts::AdjacencyGraphConcept;
  510. using boost::concepts::AdjacencyMatrixConcept;
  511. using boost::concepts::BidirectionalGraphConcept;
  512. using boost::concepts::EdgeIndexGraphConcept;
  513. using boost::concepts::EdgeListGraphConcept;
  514. using boost::concepts::EdgeMutableGraphConcept;
  515. using boost::concepts::EdgeMutablePropertyGraphConcept;
  516. using boost::concepts::GraphConcept;
  517. using boost::concepts::IncidenceGraphConcept;
  518. using boost::concepts::LvaluePropertyGraphConcept;
  519. using boost::concepts::MutableBidirectionalGraphConcept;
  520. using boost::concepts::MutableEdgeListGraphConcept;
  521. using boost::concepts::MutableGraphConcept;
  522. using boost::concepts::MutableIncidenceGraphConcept;
  523. using boost::concepts::PropertyGraphConcept;
  524. using boost::concepts::ReadablePropertyGraphConcept;
  525. using boost::concepts::VertexAndEdgeListGraphConcept;
  526. using boost::concepts::VertexIndexGraphConcept;
  527. using boost::concepts::VertexListGraphConcept;
  528. using boost::concepts::VertexMutableGraphConcept;
  529. using boost::concepts::VertexMutablePropertyGraphConcept;
  530. // Utility concepts
  531. using boost::concepts::BasicMatrixConcept;
  532. using boost::concepts::ColorValueConcept;
  533. using boost::concepts::DegreeMeasureConcept;
  534. using boost::concepts::DistanceMeasureConcept;
  535. using boost::concepts::NumericValueConcept;
  536. } /* namespace boost */
  537. #include <boost/concept/detail/concept_undef.hpp>
  538. #endif /* BOOST_GRAPH_CONCEPTS_H */