非回溯随机漫步的Kemeny常数

IF 0.9 3区数学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Random Structures & Algorithms Pub Date : 2022-03-22 DOI:10.1002/rsa.21144

Jane Breen, Nolan Faught, C. Glover, Mark Kempton, Adam Knudson, A. Oveson

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引用次数: 1

摘要

连通图G $$ G $$的Kemeny常数是随机行走到达随机选择的顶点u $$ u $$的期望时间，与初始顶点的选择无关。我们将Kemeny常数的定义扩展到非回溯随机漫步，并将其与简单随机漫步的Kemeny常数进行比较。我们探讨了几个图族的这两个参数之间的关系，并提供了正则图和双正则图的封闭形式表达式。在几乎所有情况下，非回溯的变体产生较小的凯美尼常数。

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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Kemeny's constant for nonbacktracking random walks

Kemeny's constant for a connected graph G$$ G $$ is the expected time for a random walk to reach a randomly chosen vertex u$$ u $$ , regardless of the choice of the initial vertex. We extend the definition of Kemeny's constant to nonbacktracking random walks and compare it to Kemeny's constant for simple random walks. We explore the relationship between these two parameters for several families of graphs and provide closed‐form expressions for regular and biregular graphs. In nearly all cases, the nonbacktracking variant yields the smaller Kemeny's constant.

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来源期刊

Random Structures & Algorithms 数学-计算机：软件工程

CiteScore

2.50

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： It is the aim of this journal to meet two main objectives: to cover the latest research on discrete random structures, and to present applications of such research to problems in combinatorics and computer science. The goal is to provide a natural home for a significant body of current research, and a useful forum for ideas on future studies in randomness. Results concerning random graphs, hypergraphs, matroids, trees, mappings, permutations, matrices, sets and orders, as well as stochastic graph processes and networks are presented with particular emphasis on the use of probabilistic methods in combinatorics as developed by Paul Erdõs. The journal focuses on probabilistic algorithms, average case analysis of deterministic algorithms, and applications of probabilistic methods to cryptography, data structures, searching and sorting. The journal also devotes space to such areas of probability theory as percolation, random walks and combinatorial aspects of probability.