A Faster Algorithm for Fully Dynamic Betweenness Centrality

We present a new fully dynamic algorithm for maintaining betweenness centrality (BC) of vertices in a directed graph G = (V,E) with positive edge weights. BC is a widely used parameter in the analysis of large complex networks. We achieve an amortized O(ν · log n) time per update, where n = |V | and ν bounds the number of distinct edges that lie on shortest paths through any single vertex. This result improves on the amortized bound for fully dynamic BC in [21,22] by a logarithmic factor. Our algorithm uses new data structures and techniques that are extensions of the method in the fully dynamic algorithm in Thorup [28] for APSP in graphs with unique shortest paths. For graphs with ν = O(n), our algorithm matches the fully dynamic APSP bound in Thorup [28], which holds for graphs with ν = n− 1, since it assumes unique shortest paths.