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