Commit ba2aee8a authored by Tiago Peixoto's avatar Tiago Peixoto
Browse files

* add support for betweenness centrality

* change from HashedDescriptorMap to vector_property_map in several
  algorithms to save memory and increase speed in the most common
  case, where the graph is unfiltered.




git-svn-id: https://svn.forked.de/graph-tool/trunk@102 d4600afd-f417-0410-95de-beed9576f240
parent d199d4bb
// 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
// Hacked by Tiago Peixoto, to enable openmp support for graph-tool
#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);
int i, N = num_vertices(g);
#pragma omp parallel for default(shared) private(i) schedule(dynamic)
for (i = 0; i < N; ++i)
{
typename graph_traits<Graph>::vertex_descriptor s = vertex(i, g);
if (s == graph_traits<Graph>::null_vertex())
continue;
std::stack<vertex_descriptor> ordered_vertices;
vector_property_map<typename property_traits<IncomingMap>::value_type,VertexIndexMap> incoming(vertex_index);
vector_property_map<typename property_traits<DistanceMap>::value_type,VertexIndexMap> distance(vertex_index);
vector_property_map<typename property_traits<DependencyMap>::value_type,VertexIndexMap> dependency(vertex_index);
vector_property_map<typename property_traits<PathCountMap>::value_type,VertexIndexMap> path_count(vertex_index);
// 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;
<