快速计算有向图的凯美尼常数

Haisong Xia, Zhongzhi Zhang
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引用次数: 0

摘要

图上随机行走的凯美尼常数被定义为根据静态分布随机选择的一个节点到另一个节点的平均点击时间。它已被广泛应用,并吸引了大量研究兴趣。然而,精确计算凯门尼常数需要矩阵反演,这对于拥有数百万节点的大型网络来说扩展性很差。现有的近似算法要么利用了无向图所独有的特性,要么涉及低效模拟,因此还有进一步优化的空间。为了解决有向图的这些局限性,我们提出了两种新的近似算法,用于估计有向图上的凯门尼常数,并提供理论误差保证。在真实世界网络上进行的大量数值实验验证了我们的算法在效率和准确性方面优于基线方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Fast Computation of Kemeny's Constant for Directed Graphs
Kemeny's constant for random walks on a graph is defined as the mean hitting time from one node to another selected randomly according to the stationary distribution. It has found numerous applications and attracted considerable research interest. However, exact computation of Kemeny's constant requires matrix inversion, which scales poorly for large networks with millions of nodes. Existing approximation algorithms either leverage properties exclusive to undirected graphs or involve inefficient simulation, leaving room for further optimization. To address these limitations for directed graphs, we propose two novel approximation algorithms for estimating Kemeny's constant on directed graphs with theoretical error guarantees. Extensive numerical experiments on real-world networks validate the superiority of our algorithms over baseline methods in terms of efficiency and accuracy.
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