The betweenness centrality index is essential in the analysis of social networks, but costly to compute. Currently, the fastest known algorithms require Θ(n 3 ) time and Θ(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.
In REF , the authors introduced new algorithms for computing the betweenness centrality of a vertex, which is performed in O(nm) and O(nm + n 2 log n) time for unweighted and weighted networks, respectively.
A Faster Algorithm for Betweenness Centrality
Journal of Mathematical Sociology
Mathematics