Faster Evaluation of Shortest-Path Based Centrality Indices

Abstract

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 so-called betweenness centrality index is essential for the analysis of social networks, but most costly to compute. Currently, the fastest known algorithms require O(n3) time and O(n2) space, where n is the number of vertices.<br /><br />Motivated by the fast-growing 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+nlog n)) time on unweighted or weighted graphs, respectively, where m is the number of edges. Since these algorithms simply augment single-source shortest-paths 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 networks for which centrality analysis is feasible.