Random Walks between Leaves of Random Networks

TL;DR

This paper studies the behavior and length distribution of random walks starting and ending at leaves in Erdos-Renyi and Barabasi-Albert networks, providing methods to compute walk probabilities.

Contribution

It introduces approaches to analyze walk lengths on different random network models, including node labeling techniques for probability calculations.

Findings

Walks are not transient in studied networks.

Probability of walk lengths can be computed using node labels.

Methods apply to both Erdős-Rényi and scale-free networks.

Abstract

We consider random walks that start and are absorbed on the leaves of random networks and study the length of such walks. For the networks we investigate, Erdos-Renyi random graphs and Barabasi-Albert scale free networks, these walks are not transient and we consider various approaches to computing the probability of a given length walk.One approach is to label nodes according to both their total degree and the number of links connected to leaf nodes, and as a byproduct we compute the probability of a random node of a scale free network having such a label.