Kemeny's constant for non-backtracking random walks
Combinatorics
2022-03-24 v1
Abstract
Kemeny'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 non-backtracking 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 non-backtracking variant yields the smaller Kemeny's constant.
Cite
@article{arxiv.2203.12049,
title = {Kemeny's constant for non-backtracking random walks},
author = {Jane Breen and Nolan Faught and Cory Glover and Mark Kempton and Adam Knudson and Alice Oveson},
journal= {arXiv preprint arXiv:2203.12049},
year = {2022}
}