Hitting times for non-backtracking random walks

Dario Fasino, Arianna Tonetto, Francesco Tudisco

Published 2021-05-30Version 1

A non-backtracking random walk on a graph is a random walk where, at each step, it is not allowed to return back to the node that has just been left. Non-backtracking random walks can model physical diffusion phenomena in a more realistic way than traditional random walks. However, the interest in these stochastic processes has grown only in recent years and, for this reason, there are still various open questions. In this work, we show how to compute the average number of steps a non-backtracking walker takes to reach a specific node starting from a given node. This problem can be reduced to solving a linear system that, under suitable conditions, has a unique solution. Finally, we compute the average number of steps required to perform a round trip from a given node and we show that mean return times for non-backtracking random walks coincide with their analogue for random walks in all finite, undirected graphs in which both stochastic processes are well-defined.