A Divide-and-Conquer Algorithm for Betweenness Centrality.

Given a set of target nodes S in a graph G we dene the betweenness centrality of a node v with respect to S as the fraction of shortest paths among nodes in S that contain v. For this setting we describe Brandes++, a divide-and-conquer algorithm that can eciently compute the exact values of betweenness scores. Brandes++ uses Brandes{ the most widelyused algorithm for betweenness computation { as its subroutine. It achieves the notable faster running times by applying Brandes on signicantly smaller networks than the input graph, and many of its computations can be done in parallel. The degree of speedup achieved by Brandes++ depends on the community structure of the input network as well as the size of S. Our experiments with real-life networks reveal Brandes++ achieves an average of 10-fold speedup over Brandes, while there are networks where this speedup is 75-fold. We have made our code public to benet the research community.