# Remarks on the recurrence and transience of non-backtracking random walks

## TL;DR

This paper provides a concise proof linking the recurrence properties of non-backtracking random walks to simple random walks on regular graphs and extends the proof to some irregular graphs.

## Contribution

It offers a short proof of the equivalence of recurrence between non-backtracking and simple random walks on regular graphs and extends this to certain irregular graphs.

## Key findings

- Recurrence of non-backtracking and simple random walks are equivalent on regular graphs.
- The proof can be extended to some irregular graphs.
- Provides insights into the behavior of non-backtracking walks.

## Abstract

A short proof of the equivalence of the recurrence of non-backtracking random walk and that of simple random walk on regular infinite graphs is given. It is then shown how this proof can be extended in certain cases where the graph in question is not regular.