| // Copyright 2004 The Trustees of Indiana University. | |
| // Distributed under the Boost Software License, Version 1.0. | |
| // (See accompanying file LICENSE_1_0.txt or copy at | |
| // http://www.boost.org/LICENSE_1_0.txt) | |
| // Authors: Douglas Gregor | |
| // Andrew Lumsdaine | |
| #ifndef BOOST_GRAPH_BRANDES_BETWEENNESS_CENTRALITY_HPP | |
| #define BOOST_GRAPH_BRANDES_BETWEENNESS_CENTRALITY_HPP | |
| #include <stack> | |
| #include <vector> | |
| #include <boost/graph/overloading.hpp> | |
| #include <boost/graph/dijkstra_shortest_paths.hpp> | |
| #include <boost/graph/breadth_first_search.hpp> | |
| #include <boost/graph/relax.hpp> | |
| #include <boost/graph/graph_traits.hpp> | |
| #include <boost/tuple/tuple.hpp> | |
| #include <boost/type_traits/is_convertible.hpp> | |
| #include <boost/type_traits/is_same.hpp> | |
| #include <boost/mpl/if.hpp> | |
| #include <boost/property_map/property_map.hpp> | |
| #include <boost/graph/named_function_params.hpp> | |
| #include <algorithm> | |
| namespace boost { | |
| namespace detail { namespace graph { | |
| /** | |
| * Customized visitor passed to Dijkstra's algorithm by Brandes' | |
| * betweenness centrality algorithm. This visitor is responsible for | |
| * keeping track of the order in which vertices are discovered, the | |
| * predecessors on the shortest path(s) to a vertex, and the number | |
| * of shortest paths. | |
| */ | |
| template<typename Graph, typename WeightMap, typename IncomingMap, | |
| typename DistanceMap, typename PathCountMap> | |
| struct brandes_dijkstra_visitor : public bfs_visitor<> | |
| { | |
| typedef typename graph_traits<Graph>::vertex_descriptor vertex_descriptor; | |
| typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor; | |
| brandes_dijkstra_visitor(std::stack<vertex_descriptor>& ordered_vertices, | |
| WeightMap weight, | |
| IncomingMap incoming, | |
| DistanceMap distance, | |
| PathCountMap path_count) | |
| : ordered_vertices(ordered_vertices), weight(weight), | |
| incoming(incoming), distance(distance), | |
| path_count(path_count) | |
| { } | |
| /** | |
| * Whenever an edge e = (v, w) is relaxed, the incoming edge list | |
| * for w is set to {(v, w)} and the shortest path count of w is set to | |
| * the number of paths that reach {v}. | |
| */ | |
| void edge_relaxed(edge_descriptor e, const Graph& g) | |
| { | |
| vertex_descriptor v = source(e, g), w = target(e, g); | |
| incoming[w].clear(); | |
| incoming[w].push_back(e); | |
| put(path_count, w, get(path_count, v)); | |
| } | |
| /** | |
| * If an edge e = (v, w) was not relaxed, it may still be the case | |
| * that we've found more equally-short paths, so include {(v, w)} in the | |
| * incoming edges of w and add all of the shortest paths to v to the | |
| * shortest path count of w. | |
| */ | |
| void edge_not_relaxed(edge_descriptor e, const Graph& g) | |
| { | |
| typedef typename property_traits<WeightMap>::value_type weight_type; | |
| typedef typename property_traits<DistanceMap>::value_type distance_type; | |
| vertex_descriptor v = source(e, g), w = target(e, g); | |
| distance_type d_v = get(distance, v), d_w = get(distance, w); | |
| weight_type w_e = get(weight, e); | |
| closed_plus<distance_type> combine; | |
| if (d_w == combine(d_v, w_e)) { | |
| put(path_count, w, get(path_count, w) + get(path_count, v)); | |
| incoming[w].push_back(e); | |
| } | |
| } | |
| /// Keep track of vertices as they are reached | |
| void examine_vertex(vertex_descriptor w, const Graph&) | |
| { | |
| ordered_vertices.push(w); | |
| } | |
| private: | |
| std::stack<vertex_descriptor>& ordered_vertices; | |
| WeightMap weight; | |
| IncomingMap incoming; | |
| DistanceMap distance; | |
| PathCountMap path_count; | |
| }; | |
| /** | |
| * Function object that calls Dijkstra's shortest paths algorithm | |
| * using the Dijkstra visitor for the Brandes betweenness centrality | |
| * algorithm. | |
| */ | |
| template<typename WeightMap> | |
| struct brandes_dijkstra_shortest_paths | |
| { | |
| brandes_dijkstra_shortest_paths(WeightMap weight_map) | |
| : weight_map(weight_map) { } | |
| template<typename Graph, typename IncomingMap, typename DistanceMap, | |
| typename PathCountMap, typename VertexIndexMap> | |
| void | |
| operator()(Graph& g, | |
| typename graph_traits<Graph>::vertex_descriptor s, | |
| std::stack<typename graph_traits<Graph>::vertex_descriptor>& ov, | |
| IncomingMap incoming, | |
| DistanceMap distance, | |
| PathCountMap path_count, | |
| VertexIndexMap vertex_index) | |
| { | |
| typedef brandes_dijkstra_visitor<Graph, WeightMap, IncomingMap, | |
| DistanceMap, PathCountMap> visitor_type; | |
| visitor_type visitor(ov, weight_map, incoming, distance, path_count); | |
| dijkstra_shortest_paths(g, s, | |
| boost::weight_map(weight_map) | |
| .vertex_index_map(vertex_index) | |
| .distance_map(distance) | |
| .visitor(visitor)); | |
| } | |
| private: | |
| WeightMap weight_map; | |
| }; | |
| /** | |
| * Function object that invokes breadth-first search for the | |
| * unweighted form of the Brandes betweenness centrality algorithm. | |
| */ | |
| struct brandes_unweighted_shortest_paths | |
| { | |
| /** | |
| * Customized visitor passed to breadth-first search, which | |
| * records predecessor and the number of shortest paths to each | |
| * vertex. | |
| */ | |
| template<typename Graph, typename IncomingMap, typename DistanceMap, | |
| typename PathCountMap> | |
| struct visitor_type : public bfs_visitor<> | |
| { | |
| typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor; | |
| typedef typename graph_traits<Graph>::vertex_descriptor | |
| vertex_descriptor; | |
| visitor_type(IncomingMap incoming, DistanceMap distance, | |
| PathCountMap path_count, | |
| std::stack<vertex_descriptor>& ordered_vertices) | |
| : incoming(incoming), distance(distance), | |
| path_count(path_count), ordered_vertices(ordered_vertices) { } | |
| /// Keep track of vertices as they are reached | |
| void examine_vertex(vertex_descriptor v, Graph&) | |
| { | |
| ordered_vertices.push(v); | |
| } | |
| /** | |
| * Whenever an edge e = (v, w) is labelled a tree edge, the | |
| * incoming edge list for w is set to {(v, w)} and the shortest | |
| * path count of w is set to the number of paths that reach {v}. | |
| */ | |
| void tree_edge(edge_descriptor e, Graph& g) | |
| { | |
| vertex_descriptor v = source(e, g); | |
| vertex_descriptor w = target(e, g); | |
| put(distance, w, get(distance, v) + 1); | |
| put(path_count, w, get(path_count, v)); | |
| incoming[w].push_back(e); | |
| } | |
| /** | |
| * If an edge e = (v, w) is not a tree edge, it may still be the | |
| * case that we've found more equally-short paths, so include (v, w) | |
| * in the incoming edge list of w and add all of the shortest | |
| * paths to v to the shortest path count of w. | |
| */ | |
| void non_tree_edge(edge_descriptor e, Graph& g) | |
| { | |
| vertex_descriptor v = source(e, g); | |
| vertex_descriptor w = target(e, g); | |
| if (get(distance, w) == get(distance, v) + 1) { | |
| put(path_count, w, get(path_count, w) + get(path_count, v)); | |
| incoming[w].push_back(e); | |
| } | |
| } | |
| private: | |
| IncomingMap incoming; | |
| DistanceMap distance; | |
| PathCountMap path_count; | |
| std::stack<vertex_descriptor>& ordered_vertices; | |
| }; | |
| template<typename Graph, typename IncomingMap, typename DistanceMap, | |
| typename PathCountMap, typename VertexIndexMap> | |
| void | |
| operator()(Graph& g, | |
| typename graph_traits<Graph>::vertex_descriptor s, | |
| std::stack<typename graph_traits<Graph>::vertex_descriptor>& ov, | |
| IncomingMap incoming, | |
| DistanceMap distance, | |
| PathCountMap path_count, | |
| VertexIndexMap vertex_index) | |
| { | |
| typedef typename graph_traits<Graph>::vertex_descriptor | |
| vertex_descriptor; | |
| visitor_type<Graph, IncomingMap, DistanceMap, PathCountMap> | |
| visitor(incoming, distance, path_count, ov); | |
| std::vector<default_color_type> | |
| colors(num_vertices(g), color_traits<default_color_type>::white()); | |
| boost::queue<vertex_descriptor> Q; | |
| breadth_first_visit(g, s, Q, visitor, | |
| make_iterator_property_map(colors.begin(), | |
| vertex_index)); | |
| } | |
| }; | |
| // When the edge centrality map is a dummy property map, no | |
| // initialization is needed. | |
| template<typename Iter> | |
| inline void | |
| init_centrality_map(std::pair<Iter, Iter>, dummy_property_map) { } | |
| // When we have a real edge centrality map, initialize all of the | |
| // centralities to zero. | |
| template<typename Iter, typename Centrality> | |
| void | |
| init_centrality_map(std::pair<Iter, Iter> keys, Centrality centrality_map) | |
| { | |
| typedef typename property_traits<Centrality>::value_type | |
| centrality_type; | |
| while (keys.first != keys.second) { | |
| put(centrality_map, *keys.first, centrality_type(0)); | |
| ++keys.first; | |
| } | |
| } | |
| // When the edge centrality map is a dummy property map, no update | |
| // is performed. | |
| template<typename Key, typename T> | |
| inline void | |
| update_centrality(dummy_property_map, const Key&, const T&) { } | |
| // When we have a real edge centrality map, add the value to the map | |
| template<typename CentralityMap, typename Key, typename T> | |
| inline void | |
| update_centrality(CentralityMap centrality_map, Key k, const T& x) | |
| { put(centrality_map, k, get(centrality_map, k) + x); } | |
| template<typename Iter> | |
| inline void | |
| divide_centrality_by_two(std::pair<Iter, Iter>, dummy_property_map) {} | |
| template<typename Iter, typename CentralityMap> | |
| inline void | |
| divide_centrality_by_two(std::pair<Iter, Iter> keys, | |
| CentralityMap centrality_map) | |
| { | |
| typename property_traits<CentralityMap>::value_type two(2); | |
| while (keys.first != keys.second) { | |
| put(centrality_map, *keys.first, get(centrality_map, *keys.first) / two); | |
| ++keys.first; | |
| } | |
| } | |
| template<typename Graph, typename CentralityMap, typename EdgeCentralityMap, | |
| typename IncomingMap, typename DistanceMap, | |
| typename DependencyMap, typename PathCountMap, | |
| typename VertexIndexMap, typename ShortestPaths> | |
| void | |
| brandes_betweenness_centrality_impl(const Graph& g, | |
| CentralityMap centrality, // C_B | |
| EdgeCentralityMap edge_centrality_map, | |
| IncomingMap incoming, // P | |
| DistanceMap distance, // d | |
| DependencyMap dependency, // delta | |
| PathCountMap path_count, // sigma | |
| VertexIndexMap vertex_index, | |
| ShortestPaths shortest_paths) | |
| { | |
| typedef typename graph_traits<Graph>::vertex_iterator vertex_iterator; | |
| typedef typename graph_traits<Graph>::edge_iterator edge_iterator; | |
| typedef typename graph_traits<Graph>::vertex_descriptor vertex_descriptor; | |
| // Initialize centrality | |
| init_centrality_map(vertices(g), centrality); | |
| init_centrality_map(edges(g), edge_centrality_map); | |
| std::stack<vertex_descriptor> ordered_vertices; | |
| vertex_iterator s, s_end; | |
| for (boost::tie(s, s_end) = vertices(g); s != s_end; ++s) { | |
| // Initialize for this iteration | |
| vertex_iterator w, w_end; | |
| for (boost::tie(w, w_end) = vertices(g); w != w_end; ++w) { | |
| incoming[*w].clear(); | |
| put(path_count, *w, 0); | |
| put(dependency, *w, 0); | |
| } | |
| put(path_count, *s, 1); | |
| // Execute the shortest paths algorithm. This will be either | |
| // Dijkstra's algorithm or a customized breadth-first search, | |
| // depending on whether the graph is weighted or unweighted. | |
| shortest_paths(g, *s, ordered_vertices, incoming, distance, | |
| path_count, vertex_index); | |
| while (!ordered_vertices.empty()) { | |
| vertex_descriptor w = ordered_vertices.top(); | |
| ordered_vertices.pop(); | |
| typedef typename property_traits<IncomingMap>::value_type | |
| incoming_type; | |
| typedef typename incoming_type::iterator incoming_iterator; | |
| typedef typename property_traits<DependencyMap>::value_type | |
| dependency_type; | |
| for (incoming_iterator vw = incoming[w].begin(); | |
| vw != incoming[w].end(); ++vw) { | |
| vertex_descriptor v = source(*vw, g); | |
| dependency_type factor = dependency_type(get(path_count, v)) | |
| / dependency_type(get(path_count, w)); | |
| factor *= (dependency_type(1) + get(dependency, w)); | |
| put(dependency, v, get(dependency, v) + factor); | |
| update_centrality(edge_centrality_map, *vw, factor); | |
| } | |
| if (w != *s) { | |
| update_centrality(centrality, w, get(dependency, w)); | |
| } | |
| } | |
| } | |
| typedef typename graph_traits<Graph>::directed_category directed_category; | |
| const bool is_undirected = | |
| is_convertible<directed_category*, undirected_tag*>::value; | |
| if (is_undirected) { | |
| divide_centrality_by_two(vertices(g), centrality); | |
| divide_centrality_by_two(edges(g), edge_centrality_map); | |
| } | |
| } | |
| } } // end namespace detail::graph | |
| template<typename Graph, typename CentralityMap, typename EdgeCentralityMap, | |
| typename IncomingMap, typename DistanceMap, | |
| typename DependencyMap, typename PathCountMap, | |
| typename VertexIndexMap> | |
| void | |
| brandes_betweenness_centrality(const Graph& g, | |
| CentralityMap centrality, // C_B | |
| EdgeCentralityMap edge_centrality_map, | |
| IncomingMap incoming, // P | |
| DistanceMap distance, // d | |
| DependencyMap dependency, // delta | |
| PathCountMap path_count, // sigma | |
| VertexIndexMap vertex_index | |
| BOOST_GRAPH_ENABLE_IF_MODELS_PARM(Graph,vertex_list_graph_tag)) | |
| { | |
| detail::graph::brandes_unweighted_shortest_paths shortest_paths; | |
| detail::graph::brandes_betweenness_centrality_impl(g, centrality, | |
| edge_centrality_map, | |
| incoming, distance, | |
| dependency, path_count, | |
| vertex_index, | |
| shortest_paths); | |
| } | |
| template<typename Graph, typename CentralityMap, typename EdgeCentralityMap, | |
| typename IncomingMap, typename DistanceMap, | |
| typename DependencyMap, typename PathCountMap, | |
| typename VertexIndexMap, typename WeightMap> | |
| void | |
| brandes_betweenness_centrality(const Graph& g, | |
| CentralityMap centrality, // C_B | |
| EdgeCentralityMap edge_centrality_map, | |
| IncomingMap incoming, // P | |
| DistanceMap distance, // d | |
| DependencyMap dependency, // delta | |
| PathCountMap path_count, // sigma | |
| VertexIndexMap vertex_index, | |
| WeightMap weight_map | |
| BOOST_GRAPH_ENABLE_IF_MODELS_PARM(Graph,vertex_list_graph_tag)) | |
| { | |
| detail::graph::brandes_dijkstra_shortest_paths<WeightMap> | |
| shortest_paths(weight_map); | |
| detail::graph::brandes_betweenness_centrality_impl(g, centrality, | |
| edge_centrality_map, | |
| incoming, distance, | |
| dependency, path_count, | |
| vertex_index, | |
| shortest_paths); | |
| } | |
| namespace detail { namespace graph { | |
| template<typename Graph, typename CentralityMap, typename EdgeCentralityMap, | |
| typename WeightMap, typename VertexIndexMap> | |
| void | |
| brandes_betweenness_centrality_dispatch2(const Graph& g, | |
| CentralityMap centrality, | |
| EdgeCentralityMap edge_centrality_map, | |
| WeightMap weight_map, | |
| VertexIndexMap vertex_index) | |
| { | |
| typedef typename graph_traits<Graph>::degree_size_type degree_size_type; | |
| typedef typename graph_traits<Graph>::vertex_descriptor vertex_descriptor; | |
| typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor; | |
| typedef typename mpl::if_c<(is_same<CentralityMap, | |
| dummy_property_map>::value), | |
| EdgeCentralityMap, | |
| CentralityMap>::type a_centrality_map; | |
| typedef typename property_traits<a_centrality_map>::value_type | |
| centrality_type; | |
| typename graph_traits<Graph>::vertices_size_type V = num_vertices(g); | |
| std::vector<std::vector<edge_descriptor> > incoming(V); | |
| std::vector<centrality_type> distance(V); | |
| std::vector<centrality_type> dependency(V); | |
| std::vector<degree_size_type> path_count(V); | |
| brandes_betweenness_centrality( | |
| g, centrality, edge_centrality_map, | |
| make_iterator_property_map(incoming.begin(), vertex_index), | |
| make_iterator_property_map(distance.begin(), vertex_index), | |
| make_iterator_property_map(dependency.begin(), vertex_index), | |
| make_iterator_property_map(path_count.begin(), vertex_index), | |
| vertex_index, | |
| weight_map); | |
| } | |
| template<typename Graph, typename CentralityMap, typename EdgeCentralityMap, | |
| typename VertexIndexMap> | |
| void | |
| brandes_betweenness_centrality_dispatch2(const Graph& g, | |
| CentralityMap centrality, | |
| EdgeCentralityMap edge_centrality_map, | |
| VertexIndexMap vertex_index) | |
| { | |
| typedef typename graph_traits<Graph>::degree_size_type degree_size_type; | |
| typedef typename graph_traits<Graph>::vertex_descriptor vertex_descriptor; | |
| typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor; | |
| typedef typename mpl::if_c<(is_same<CentralityMap, | |
| dummy_property_map>::value), | |
| EdgeCentralityMap, | |
| CentralityMap>::type a_centrality_map; | |
| typedef typename property_traits<a_centrality_map>::value_type | |
| centrality_type; | |
| typename graph_traits<Graph>::vertices_size_type V = num_vertices(g); | |
| std::vector<std::vector<edge_descriptor> > incoming(V); | |
| std::vector<centrality_type> distance(V); | |
| std::vector<centrality_type> dependency(V); | |
| std::vector<degree_size_type> path_count(V); | |
| brandes_betweenness_centrality( | |
| g, centrality, edge_centrality_map, | |
| make_iterator_property_map(incoming.begin(), vertex_index), | |
| make_iterator_property_map(distance.begin(), vertex_index), | |
| make_iterator_property_map(dependency.begin(), vertex_index), | |
| make_iterator_property_map(path_count.begin(), vertex_index), | |
| vertex_index); | |
| } | |
| template<typename WeightMap> | |
| struct brandes_betweenness_centrality_dispatch1 | |
| { | |
| template<typename Graph, typename CentralityMap, | |
| typename EdgeCentralityMap, typename VertexIndexMap> | |
| static void | |
| run(const Graph& g, CentralityMap centrality, | |
| EdgeCentralityMap edge_centrality_map, VertexIndexMap vertex_index, | |
| WeightMap weight_map) | |
| { | |
| brandes_betweenness_centrality_dispatch2(g, centrality, edge_centrality_map, | |
| weight_map, vertex_index); | |
| } | |
| }; | |
| template<> | |
| struct brandes_betweenness_centrality_dispatch1<error_property_not_found> | |
| { | |
| template<typename Graph, typename CentralityMap, | |
| typename EdgeCentralityMap, typename VertexIndexMap> | |
| static void | |
| run(const Graph& g, CentralityMap centrality, | |
| EdgeCentralityMap edge_centrality_map, VertexIndexMap vertex_index, | |
| error_property_not_found) | |
| { | |
| brandes_betweenness_centrality_dispatch2(g, centrality, edge_centrality_map, | |
| vertex_index); | |
| } | |
| }; | |
| template <typename T> | |
| struct is_bgl_named_params { | |
| BOOST_STATIC_CONSTANT(bool, value = false); | |
| }; | |
| template <typename Param, typename Tag, typename Rest> | |
| struct is_bgl_named_params<bgl_named_params<Param, Tag, Rest> > { | |
| BOOST_STATIC_CONSTANT(bool, value = true); | |
| }; | |
| } } // end namespace detail::graph | |
| template<typename Graph, typename Param, typename Tag, typename Rest> | |
| void | |
| brandes_betweenness_centrality(const Graph& g, | |
| const bgl_named_params<Param,Tag,Rest>& params | |
| BOOST_GRAPH_ENABLE_IF_MODELS_PARM(Graph,vertex_list_graph_tag)) | |
| { | |
| typedef bgl_named_params<Param,Tag,Rest> named_params; | |
| typedef typename property_value<named_params, edge_weight_t>::type ew; | |
| detail::graph::brandes_betweenness_centrality_dispatch1<ew>::run( | |
| g, | |
| choose_param(get_param(params, vertex_centrality), | |
| dummy_property_map()), | |
| choose_param(get_param(params, edge_centrality), | |
| dummy_property_map()), | |
| choose_const_pmap(get_param(params, vertex_index), g, vertex_index), | |
| get_param(params, edge_weight)); | |
| } | |
| // disable_if is required to work around problem with MSVC 7.1 (it seems to not | |
| // get partial ordering getween this overload and the previous one correct) | |
| template<typename Graph, typename CentralityMap> | |
| typename disable_if<detail::graph::is_bgl_named_params<CentralityMap>, | |
| void>::type | |
| brandes_betweenness_centrality(const Graph& g, CentralityMap centrality | |
| BOOST_GRAPH_ENABLE_IF_MODELS_PARM(Graph,vertex_list_graph_tag)) | |
| { | |
| detail::graph::brandes_betweenness_centrality_dispatch2( | |
| g, centrality, dummy_property_map(), get(vertex_index, g)); | |
| } | |
| template<typename Graph, typename CentralityMap, typename EdgeCentralityMap> | |
| void | |
| brandes_betweenness_centrality(const Graph& g, CentralityMap centrality, | |
| EdgeCentralityMap edge_centrality_map | |
| BOOST_GRAPH_ENABLE_IF_MODELS_PARM(Graph,vertex_list_graph_tag)) | |
| { | |
| detail::graph::brandes_betweenness_centrality_dispatch2( | |
| g, centrality, edge_centrality_map, get(vertex_index, g)); | |
| } | |
| /** | |
| * Converts "absolute" betweenness centrality (as computed by the | |
| * brandes_betweenness_centrality algorithm) in the centrality map | |
| * into "relative" centrality. The result is placed back into the | |
| * given centrality map. | |
| */ | |
| template<typename Graph, typename CentralityMap> | |
| void | |
| relative_betweenness_centrality(const Graph& g, CentralityMap centrality) | |
| { | |
| typedef typename graph_traits<Graph>::vertex_iterator vertex_iterator; | |
| typedef typename property_traits<CentralityMap>::value_type centrality_type; | |
| typename graph_traits<Graph>::vertices_size_type n = num_vertices(g); | |
| centrality_type factor = centrality_type(2)/centrality_type(n*n - 3*n + 2); | |
| vertex_iterator v, v_end; | |
| for (boost::tie(v, v_end) = vertices(g); v != v_end; ++v) { | |
| put(centrality, *v, factor * get(centrality, *v)); | |
| } | |
| } | |
| // Compute the central point dominance of a graph. | |
| template<typename Graph, typename CentralityMap> | |
| typename property_traits<CentralityMap>::value_type | |
| central_point_dominance(const Graph& g, CentralityMap centrality | |
| BOOST_GRAPH_ENABLE_IF_MODELS_PARM(Graph,vertex_list_graph_tag)) | |
| { | |
| using std::max; | |
| typedef typename graph_traits<Graph>::vertex_iterator vertex_iterator; | |
| typedef typename property_traits<CentralityMap>::value_type centrality_type; | |
| typename graph_traits<Graph>::vertices_size_type n = num_vertices(g); | |
| // Find max centrality | |
| centrality_type max_centrality(0); | |
| vertex_iterator v, v_end; | |
| for (boost::tie(v, v_end) = vertices(g); v != v_end; ++v) { | |
| max_centrality = (max)(max_centrality, get(centrality, *v)); | |
| } | |
| // Compute central point dominance | |
| centrality_type sum(0); | |
| for (boost::tie(v, v_end) = vertices(g); v != v_end; ++v) { | |
| sum += (max_centrality - get(centrality, *v)); | |
| } | |
| return sum/(n-1); | |
| } | |
| } // end namespace boost | |
| #endif // BOOST_GRAPH_BRANDES_BETWEENNESS_CENTRALITY_HPP |