Weighted Enumeration of Nonbacktracking Walks on Weighted Graphs

IF 1.5 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-01-30 DOI:10.1137/23m155219x

Francesca Arrigo, Desmond J. Higham, Vanni Noferini, Ryan Wood

引用次数: 0

Abstract

SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 397-418, March 2024.
Abstract. We extend the notion of nonbacktracking walks from unweighted graphs to graphs whose edges have a nonnegative weight. Here the weight associated with a walk is taken to be the product over the weights along the individual edges. We give two ways to compute the associated generating function, and corresponding node centrality measures. One method works directly on the original graph and one uses a line graph construction followed by a projection. The first method is more efficient, but the second has the advantage of extending naturally to time-evolving graphs. Based on these generating functions, we define and study corresponding centrality measures. Illustrative computational results are also provided.

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加权图上非回溯行走的加权枚举

SIAM 矩阵分析与应用期刊》，第 45 卷，第 1 期，第 397-418 页，2024 年 3 月。摘要我们将无权重图中的非回溯走行概念扩展到边具有非负权重的图。在这里，与走行相关的权重是各条边权重的乘积。我们给出了两种计算相关生成函数和相应节点中心度量的方法。一种方法是直接计算原始图，另一种方法是先构建线图，然后进行投影。第一种方法更有效，但第二种方法的优点是可以自然扩展到时间演化图。基于这些生成函数，我们定义并研究了相应的中心性度量。我们还提供了示例性计算结果。

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.