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arxiv:2510.06650
On defining Kemeny's constant for non-backtracking random walks
Published on Oct 8, 2025
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Abstract
The study defines and compares two versions of Kemeny's constant using non-backtracking random walks, analyzing equality conditions and differences across graph families.
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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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