Entropy Rate of Diffusion Processes on Complex Networks

TL;DR

This paper introduces the entropy rate for diffusion processes on complex networks, analyzing how network structure influences diffusion randomness and proposing methods to optimize entropy for various real-world networks.

Contribution

It presents a novel entropy rate concept for diffusion on networks, linking network heterogeneity and correlations to diffusion randomness, and offers a framework for designing optimal diffusion processes.

Findings

Degree heterogeneity affects entropy rate significantly.

Correlations between node degrees influence diffusion entropy.

Method to maximize entropy for given network structures.

Abstract

The concept of entropy rate for a dynamical process on a graph is introduced. We study diffusion processes where the node degrees are used as a local information by the random walkers. We describe analitically and numerically how the degree heterogeneity and correlations affect the diffusion entropy rate. In addition, the entropy rate is used to characterize complex networks from the real world. Our results point out how to design optimal diffusion processes that maximize the entropy for a given network structure, providing a new theoretical tool with applications to social, technological and communication networks.