Finding hitting times in various graphs

TL;DR

This paper introduces two methods for calculating hitting times in finite graphs and explores their applications to various graph classes like grids, trees, and tadpole graphs.

Contribution

It presents novel methods for computing hitting times and applies them to different graph structures, expanding understanding of random walk behaviors.

Findings

Two methods for calculating hitting times are proposed.

Applications demonstrated on grids, trees, and tadpole graphs.

Enhanced understanding of random walk dynamics in various graph types.

Abstract

The hitting time, h_uv, of a random walk on a finite graph G, is the expected time for the walk to reach vertex v given that it started at vertex u. We present two methods of calculating the hitting time between vertices of finite graphs, along with applications to specific classes of graphs, including grids, trees, and the 'tadpole' graphs.