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