boost/graph/betweenness_centrality.hpp
// 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>::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>::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>::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<param_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, param_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 get_param_type<edge_weight_t, named_params>::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