Hitting Times of Random Walks on Edge Corona Product Graphs

TL;DR

This paper investigates the hitting times of random walks on graphs formed by iterative edge corona products, deriving recursive eigenvalue solutions and formulas for hitting times and Kemeny's constant.

Contribution

It introduces recursive methods for eigenvalues and explicit formulas for hitting times on edge corona product graphs, advancing understanding of random walks on complex network models.

Findings

Derived recursive solutions for eigenvalues and eigenvectors.

Provided formulas for two-node hitting times and Kemeny's constant.

Analyzed hitting times on iteratively constructed edge corona graphs.

Abstract

Graph products have been extensively applied to model complex networks with striking properties observed in real-world complex systems. In this paper, we study the hitting times for random walks on a class of graphs generated iteratively by edge corona product. We first derive recursive solutions to the eigenvalues and eigenvectors of the normalized adjacency matrix associated with the graphs. Based on these results, we further obtain interesting quantities about hitting times of random walks, providing iterative formulas for two-node hitting time, as well as closed-form expressions for the Kemeny's constant defined as a weighted average of hitting times over all node pairs, as well as the arithmetic mean of hitting times of all pairs of nodes.