1 // Copyright 2004 The Trustees of Indiana University.
2
3 // Use, modification and distribution is subject to the Boost Software
4 // License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
5 // http://www.boost.org/LICENSE_1_0.txt)
6
7 // Authors: Douglas Gregor
8 // Andrew Lumsdaine
9 #ifndef BOOST_GRAPH_BETWEENNESS_CENTRALITY_CLUSTERING_HPP
10 #define BOOST_GRAPH_BETWEENNESS_CENTRALITY_CLUSTERING_HPP
11
12 #include <boost/graph/betweenness_centrality.hpp>
13 #include <boost/graph/graph_traits.hpp>
14 #include <boost/pending/indirect_cmp.hpp>
15 #include <algorithm>
16 #include <vector>
17 #include <boost/property_map.hpp>
18
19 namespace boost {
20
21 /** Threshold termination function for the betweenness centrality
22 * clustering algorithm.
23 */
24 template<typename T>
25 struct bc_clustering_threshold
26 {
27 typedef T centrality_type;
28
29 /// Terminate clustering when maximum absolute edge centrality is
30 /// below the given threshold.
bc_clustering_thresholdboost::bc_clustering_threshold31 explicit bc_clustering_threshold(T threshold)
32 : threshold(threshold), dividend(1.0) {}
33
34 /**
35 * Terminate clustering when the maximum edge centrality is below
36 * the given threshold.
37 *
38 * @param threshold the threshold value
39 *
40 * @param g the graph on which the threshold will be calculated
41 *
42 * @param normalize when true, the threshold is compared against the
43 * normalized edge centrality based on the input graph; otherwise,
44 * the threshold is compared against the absolute edge centrality.
45 */
46 template<typename Graph>
bc_clustering_thresholdboost::bc_clustering_threshold47 bc_clustering_threshold(T threshold, const Graph& g, bool normalize = true)
48 : threshold(threshold), dividend(1.0)
49 {
50 if (normalize) {
51 typename graph_traits<Graph>::vertices_size_type n = num_vertices(g);
52 dividend = T((n - 1) * (n - 2)) / T(2);
53 }
54 }
55
56 /** Returns true when the given maximum edge centrality (potentially
57 * normalized) falls below the threshold.
58 */
59 template<typename Graph, typename Edge>
operator ()boost::bc_clustering_threshold60 bool operator()(T max_centrality, Edge, const Graph&)
61 {
62 return (max_centrality / dividend) < threshold;
63 }
64
65 protected:
66 T threshold;
67 T dividend;
68 };
69
70 /** Graph clustering based on edge betweenness centrality.
71 *
72 * This algorithm implements graph clustering based on edge
73 * betweenness centrality. It is an iterative algorithm, where in each
74 * step it compute the edge betweenness centrality (via @ref
75 * brandes_betweenness_centrality) and removes the edge with the
76 * maximum betweenness centrality. The @p done function object
77 * determines when the algorithm terminates (the edge found when the
78 * algorithm terminates will not be removed).
79 *
80 * @param g The graph on which clustering will be performed. The type
81 * of this parameter (@c MutableGraph) must be a model of the
82 * VertexListGraph, IncidenceGraph, EdgeListGraph, and Mutable Graph
83 * concepts.
84 *
85 * @param done The function object that indicates termination of the
86 * algorithm. It must be a ternary function object thats accepts the
87 * maximum centrality, the descriptor of the edge that will be
88 * removed, and the graph @p g.
89 *
90 * @param edge_centrality (UTIL/OUT) The property map that will store
91 * the betweenness centrality for each edge. When the algorithm
92 * terminates, it will contain the edge centralities for the
93 * graph. The type of this property map must model the
94 * ReadWritePropertyMap concept. Defaults to an @c
95 * iterator_property_map whose value type is
96 * @c Done::centrality_type and using @c get(edge_index, g) for the
97 * index map.
98 *
99 * @param vertex_index (IN) The property map that maps vertices to
100 * indices in the range @c [0, num_vertices(g)). This type of this
101 * property map must model the ReadablePropertyMap concept and its
102 * value type must be an integral type. Defaults to
103 * @c get(vertex_index, g).
104 */
105 template<typename MutableGraph, typename Done, typename EdgeCentralityMap,
106 typename VertexIndexMap>
107 void
betweenness_centrality_clustering(MutableGraph & g,Done done,EdgeCentralityMap edge_centrality,VertexIndexMap vertex_index)108 betweenness_centrality_clustering(MutableGraph& g, Done done,
109 EdgeCentralityMap edge_centrality,
110 VertexIndexMap vertex_index)
111 {
112 typedef typename property_traits<EdgeCentralityMap>::value_type
113 centrality_type;
114 typedef typename graph_traits<MutableGraph>::edge_iterator edge_iterator;
115 typedef typename graph_traits<MutableGraph>::edge_descriptor edge_descriptor;
116 typedef typename graph_traits<MutableGraph>::vertices_size_type
117 vertices_size_type;
118
119 if (edges(g).first == edges(g).second) return;
120
121 // Function object that compares the centrality of edges
122 indirect_cmp<EdgeCentralityMap, std::less<centrality_type> >
123 cmp(edge_centrality);
124
125 bool is_done;
126 do {
127 brandes_betweenness_centrality(g,
128 edge_centrality_map(edge_centrality)
129 .vertex_index_map(vertex_index));
130 edge_descriptor e = *max_element(edges(g).first, edges(g).second, cmp);
131 is_done = done(get(edge_centrality, e), e, g);
132 if (!is_done) remove_edge(e, g);
133 } while (!is_done && edges(g).first != edges(g).second);
134 }
135
136 /**
137 * \overload
138 */
139 template<typename MutableGraph, typename Done, typename EdgeCentralityMap>
140 void
betweenness_centrality_clustering(MutableGraph & g,Done done,EdgeCentralityMap edge_centrality)141 betweenness_centrality_clustering(MutableGraph& g, Done done,
142 EdgeCentralityMap edge_centrality)
143 {
144 betweenness_centrality_clustering(g, done, edge_centrality,
145 get(vertex_index, g));
146 }
147
148 /**
149 * \overload
150 */
151 template<typename MutableGraph, typename Done>
152 void
betweenness_centrality_clustering(MutableGraph & g,Done done)153 betweenness_centrality_clustering(MutableGraph& g, Done done)
154 {
155 typedef typename Done::centrality_type centrality_type;
156 std::vector<centrality_type> edge_centrality(num_edges(g));
157 betweenness_centrality_clustering(g, done,
158 make_iterator_property_map(edge_centrality.begin(), get(edge_index, g)),
159 get(vertex_index, g));
160 }
161
162 } // end namespace boost
163
164 #endif // BOOST_GRAPH_BETWEENNESS_CENTRALITY_CLUSTERING_HPP
165