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arXiv · 2203.12049

Kemeny's constant for non-backtracking random walks

Jane Breen·Nolan Faught·Cory Glover·Mark Kempton·Adam Knudson·Alice Oveson
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Abstract

Kemeny's constant for a connected graph $G$ is the expected time for a random walk to reach a randomly-chosen vertex $u$, 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.

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Jane Breen, Nolan Faught, Cory Glover, Mark Kempton, Adam Knudson, Alice Oveson. 2022-03-22. Kemeny's constant for non-backtracking random walks. https://arxiv.org/abs/2203.12049

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