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A Faster Algorithm for Betweenness Centrality
 Journal of Mathematical Sociology
, 2001
"... The betweenness centrality index is essential in the analysis of social networks, but costly to compute. Currently, the fastest known algorithms require #(n ) time and #(n ) space, where n is the number of actors in the network. ..."
Abstract

Cited by 334 (5 self)
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The betweenness centrality index is essential in the analysis of social networks, but costly to compute. Currently, the fastest known algorithms require #(n ) time and #(n ) space, where n is the number of actors in the network.
Faster Evaluation of ShortestPath Based Centrality Indices
, 2000
"... Centrality indices are an important tool in network analysis, and many of them are derived from the set of all shortest paths of the underlying graph. The socalled betweenness centrality index is essential for the analysis of social networks, but most costly to compute. Currently, the fastest known ..."
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Cited by 2 (0 self)
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Centrality indices are an important tool in network analysis, and many of them are derived from the set of all shortest paths of the underlying graph. The socalled betweenness centrality index is essential for the analysis of social networks, but most costly to compute. Currently, the fastest known algorithms require Theta(n³) time and Theta(n²) space, where n is the number of vertices. Motivated by the fastgrowing need to compute centrality indices on large, yet very sparse, networks, new algorithms for betweenness are introduced in this paper. They require O(n + m) space and run in O(n(m + n)) or O(n(m + n log n)) time on unweighted or weighted graphs, respectively, where m is the number of edges. Since these algorithms simply augment singlesource shortestpaths computations, all standard centrality indices based on shortest paths can now be computed uniformly in one framework. Experimental evidence is provided that this substantially increases the range of network...