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arXiv · 2510.06650

On defining Kemeny's constant for non-backtracking random walks

Jane Breen·Mark Kempton·Adam Knudson·Matthew Shumway
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Abstract

We propose two possible definitions for a version of Kemeny's constant of a graph based on non-backtracking random walks (in place of the usual simple random walk). We show that these two definitions coincide for edge-transitive graphs, and give a condition generalizing edge-transitive for which equality holds, and investigate by how much they can differ in general. We compute our non-backtracking Kemeny's constant for several families of graphs.

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Jane Breen, Mark Kempton, Adam Knudson, Matthew Shumway. 2025-10-08. On defining Kemeny's constant for non-backtracking random walks. https://arxiv.org/abs/2510.06650

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