An algorithm for updating betweenness centrality scores of all vertices in a graph upon deletion of a single edge

Abstract

Betweenness centrality (BC) is a measure of the importance of a vertex in a graph, which is defined using the number of the shortest paths passing through the vertex. Brandes proposed an efficient algorithm for computing the BC scores of all vertices in a graph, which accumulates pair dependencies while traversing single-source shortest paths. Although this algorithm works well on static graphs, its direct application to dynamic graphs takes a huge amount of computation time because the BC scores must be computed from scratch every time the structure of graph changes. Therefore, various algorithms for updating the BC scores of all vertices have been developed so far. In this article, we propose a novel algorithm for updating the BC scores of all vertices in a graph upon deletion of a single edge. We also show the validity and efficiency of the proposed algorithm through theoretical analysis and experiments using various graphs obtained from synthetic and real networks.