Kemeny's constant for nonbacktracking random walks

Abstract

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.