Current Flow Group Closeness Centrality for Complex Networks

Current flow closeness centrality (CFCC) has a better discriminating ability than the ordinary closeness centrality based on shortest paths. In this paper, we extend this notion to a group of vertices in a weighted graph, and then study the problem of finding a subset S of k vertices to maximize its CFCC C(S), both theoretically and experimentally. We show that the problem is NP-hard, but propose two greedy algorithms for minimizing the reciprocal of C(S) with provable guarantees using the monotoncity and supermodularity. The first is a deterministic algorithm with an approximation factor (1-frackk-1·frac1e) and cubic running time; while the second is a randomized algorithm with a (1-frackk-1·frac1e-ε)-approximation and nearly-linear running time for any ε > 0. Extensive experiments on model and real networks demonstrate that our algorithms are effective and efficient, with the second algorithm being scalable to massive networks with more than a million vertices.