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.
Brandes proposed the fastest known algorithm that runs in OðjV jjEjÞ time REF ; see Section 2.1 for details.
A Faster Algorithm for Betweenness Centrality
Journal of Mathematical Sociology
Mathematics