复杂网络的电流群封闭中心性
Current Flow Group Closeness Centrality for Complex Networks
摘要：
与基于最短路径的贴近中心度相比，电流贴近中心度具有更好的区分能力。在本文中，我们将这一概念扩展到一组加权图的顶点，然后研究的问题，找到一个子集$S$的$k$顶点，以最大化其CFCC $C(S)$，从理论和实验。我们表明，该问题是NP-难的，但提出了两个贪心算法最小化的倒数$C(S)$证明保证使用单调性和超模块性。第一个是一个确定性算法的近似因子$(1-\frac{k}{k-1}\cdot\frac{1}{e})$和立方运行时间，而第二个是一个随机算法的$(1-\frac{k}{k-1}\cdot\frac{1}{e}-ε)$近似和近线性运行时间的任何$ε> 0$。在模型和真实网络上的大量实验表明，我们的算法是有效的和高效的，与第二个算法是可扩展的大规模网络与超过一百万个顶点。
英文摘要：
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 $(1-\frac{k}{k-1}\cdot\frac{1}{e}-ε)$-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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
