An Escape Time Formulation for Subgraph Detection and Partitioning of Directed Graphs

IF 1.5 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-02-26 DOI:10.1137/23m1553790

Zachary M. Boyd, Nicolas Fraiman, Jeremy L. Marzuola, Peter J. Mucha, Braxton Osting

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引用次数: 0

Abstract

SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 685-711, March 2024.
Abstract. We provide a rearrangement based algorithm for detection of subgraphs of k vertices with long escape times for directed or undirected networks that is not combinatorially complex to compute. Complementing other notions of densest subgraphs and graph cuts, our method is based on the mean hitting time required for a random walker to leave a designated set and hit the complement. We provide a new relaxation of this notion of hitting time on a given subgraph and use that relaxation to construct a subgraph detection algorithm that can be computed easily and a generalization to K-partitioning schemes. Using a modification of the subgraph detector on each component, we propose a graph partitioner that identifies regions where random walks live for comparably large times. Importantly, our method implicitly respects the directed nature of the data for directed graphs while also being applicable to undirected graphs. We apply the partitioning method for community detection to a large class of models and real-world data sets.

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有向图的子图检测和分割的逃逸时间公式

SIAM 矩阵分析与应用期刊》，第 45 卷，第 1 期，第 685-711 页，2024 年 3 月。摘要。我们提供了一种基于重排的算法，用于检测有向或无向网络中逃逸时间较长的 k 个顶点的子图，其计算并不复杂。作为对其他最密子图和图切割概念的补充，我们的方法基于随机漫步者离开指定集合并命中补集所需的平均命中时间。我们对给定子图上的命中时间这一概念进行了新的松弛，并利用这一松弛构建了一种可以轻松计算的子图检测算法，并将其推广到 K 分区方案中。利用对每个组件上的子图检测器的修改，我们提出了一种图分割器，它能识别随机游走存活时间相当大的区域。重要的是，我们的方法隐含地尊重了有向图数据的有向性，同时也适用于无向图。我们将群落检测的分区方法应用于一大类模型和真实世界的数据集。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Matrix Analysis and Applications 数学-应用数学

CiteScore

2.90

自引率

6.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Matrix Analysis and Applications contains research articles in matrix analysis and its applications and papers of interest to the numerical linear algebra community. Applications include such areas as signal processing, systems and control theory, statistics, Markov chains, and mathematical biology. Also contains papers that are of a theoretical nature but have a possible impact on applications.