Papers › Current Flow Group Closeness Centrality for Complex Networks
Current Flow Group Closeness Centrality for Complex Networks
Huan Li, Richard Peng, Liren Shan, Yuhao Yi, Zhongzhi Zhang
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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-k/(k-1)·1/e) and cubic running time; while the second is a randomized algorithm with a (1-k/(k-1)·1/e-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.
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