--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/epoc32/include/stdapis/boost/graph/betweenness_centrality.hpp Tue Mar 16 16:12:26 2010 +0000
@@ -0,0 +1,599 @@
+// 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/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.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 (tie(s, s_end) = vertices(g); s != s_end; ++s) {
+ // Initialize for this iteration
+ vertex_iterator w, w_end;
+ for (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)
+{
+ 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)
+{
+ 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);
+ }
+ };
+
+} } // 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)
+{
+ 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));
+}
+
+template<typename Graph, typename CentralityMap>
+void
+brandes_betweenness_centrality(const Graph& g, CentralityMap centrality)
+{
+ 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)
+{
+ 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 (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)
+{
+ 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 (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 (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