A faster algorithm for betweenness centrality

The betweenness centrality index is essential in the analysis of social networks, but costly to compute. Currently, the fastest known algorithms require circle minus (n(3)) time and circle minus (n(2)) space, where n is the number of actors in the network. 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(nm) and O(nm + n(2) log n) time on unweighted and weighted networks, respectively, where m is the number of links. Experimental evidence is provided that this substantially increases the range of networks for which centrality analysis is feasible.