Betweenness Centrality - Incremental and Faster

We present an incremental algorithm that updates the betweenness centrality (BC) score of all vertices in a graph G when a new edge is added to G, or the weight of an existing edge is reduced. Our incremental algorithm runs in O(ν∗ · n) time, where ν∗ is bounded by m∗, the number of edges that lie on a shortest path in G. We achieve the same bound for the more general incremental vertex update problem. Even for a single edge update, our incremental algorithm is the first algorithm that is provably faster on sparse graphs than recomputing with the well-known static Brandes algorithm. It is also likely to be much faster than Brandes on dense graphs since m∗ is often close to linear in n. Our incremental algorithm is very simple, and we give an efficient cache-oblivious implementation that incurs O(n · sort(ν∗)) cache misses, where sort is a well-known measure for caching efficiency.