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arXiv · 1802.02556

Current Flow Group Closeness Centrality for Complex Networks

Huan Li·Richard Peng·Liren Shan·Yuhao Yi·Zhongzhi Zhang
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Abstract

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 $(1-\frac{k}{k-1}\cdot\frac{1}{e})$ and cubic running time; while the second is a randomized algorithm with a $(1-\frac{k}{k-1}\cdot\frac{1}{e}-\epsilon)$-approximation and nearly-linear running time for any $\epsilon > 0$. 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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Huan Li, Richard Peng, Liren Shan, Yuhao Yi, Zhongzhi Zhang. 2018-02-07. Current Flow Group Closeness Centrality for Complex Networks. https://doi.org/10.1145/3308558.3313490

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