SILVAN: Estimating Betweenness Centralities with Progressive Sampling and Non-uniform Rademacher Bounds

Betweenness centrality is a popular centrality measure with applications in several domains, and whose exact computation is impractical for modern-sized networks. We present SILVAN, a novel, efficient algorithm to compute, with high probability, accurate estimates of the betweenness centrality of all nodes of a graph and a high-quality approximation of the k most central nodes of a graph. SILVAN follows a progressive sampling approach, and builds on recently improved bounds on Monte-Carlo Empirical Rademacher Averages, a fundamental tool from statistical learning theory. SILVAN relies on a novel estimation scheme that leads to non-uniform bounds on the deviation of the estimates from the true values of the between centrality of all the nodes, providing tight guarantees on the quality of the approximation. Our extensive experimental evaluation shows that SILVAN extracts high-quality approximations while outperforming, in terms of number of samples and accuracy, the state-of-the-art approximation algorithm with comparable quality guarantees.