Maximal-entropy random walks in complex networks with limited information

TL;DR

This paper shows how to construct near-maximal-entropy random walks in complex networks using only local information, with step probabilities related to node degrees and network correlations.

Contribution

It introduces a method to create maximal-entropy random walks based solely on local graph information, adapting to degree correlations.

Findings

Almost maximal-entropy walks have step probabilities proportional to node degree raised to a power.

The exponent for the degree power depends on degree-degree correlations.

In uncorrelated graphs, the exponent is exactly 1.

Abstract

Maximization of the entropy rate is an important issue to design diffusion processes aiming at a well-mixed state. We demonstrate that it is possible to construct maximal-entropy random walks with only local information on the graph structure. In particular, we show that an almost maximal-entropy random walk is obtained when the step probabilities are proportional to a power of the degree of the target node, with an exponent $\alpha$ that depends on the degree-degree correlations, and is equal to 1 in uncorrelated graphs.