Kemeny's constant for nonbacktracking random walks-Reference-Cited by-同舟云学术

Kemeny's constant for nonbacktracking random walks

Published:2023-02-24 Issue:2 Volume:63 Page:343-363
ISSN:1042-9832
Container-title:Random Structures & Algorithms
language:en
Short-container-title:Random Struct Algorithms

Author:

Breen Jane¹,Faught Nolan²,Glover Cory³,Kempton Mark²,Knudson Adam²,Oveson Alice²

Affiliation:

1. Faculty of Science Ontario Tech University Oshawa Ontario Canada

2. Department of Mathematics Brigham Young University Provo Utah USA

3. Network Science Institute Northeastern University Boston Massachusetts USA

Abstract

AbstractKemeny's constant for a connected graph is the expected time for a random walk to reach a randomly chosen vertex , 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.

Publisher

Wiley

Subject

Applied Mathematics,Computer Graphics and Computer-Aided Design,General Mathematics,Software

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1002/rsa.21144

Reference18 articles.

1. D.AldousandJ. A.Fill Reversible Markov chains and random walks on graphs 2002. Unfinished monograph recompiled 2014 http://www.stat.berkeley.edu/∼aldous/RWG/book.html.

2. NON-BACKTRACKING RANDOM WALKS MIX FASTER

3. Non-backtracking PageRank

4. Graphs and Matrices

5. Computing Kemeny's constant for a barbell graph

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