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...

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Bibliographic Details
Published inRandom structures & algorithms Vol. 63; no. 2; pp. 343 - 363
Main Authors Breen, Jane, Faught, Nolan, Glover, Cory, Kempton, Mark, Knudson, Adam, Oveson, Alice
Format Journal Article
LanguageEnglish
Published New York John Wiley & Sons, Inc 01.09.2023
Wiley Subscription Services, Inc
Subjects
Graphs
Kemeny's constant
nonbacktracking walks
Random walk
regular graphs
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Summary: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.
ISSN:1042-9832
1098-2418
DOI:10.1002/rsa.21144