Mean-field diffusive dynamics on weighted networks

TL;DR

This paper introduces a formalism for deriving mean-field equations for diffusive processes on weighted networks, highlighting its accuracy on annealed networks and limitations on real scale-free networks.

Contribution

The authors develop a general mean-field formalism for diffusive dynamics on weighted networks and introduce annealed weighted networks where these equations are exact.

Findings

Mean-field equations accurately describe annealed weighted networks.

Significant deviations occur between mean-field predictions and real scale-free networks.

The formalism can be extended to complex diffusive dynamics.

Abstract

Diffusion is a key element of a large set of phenomena occurring on natural and social systems modeled in terms of complex weighted networks. Here, we introduce a general formalism that allows to easily write down mean-field equations for any diffusive dynamics on weighted networks. We also propose the concept of annealed weighted networks, in which such equations become exact. We show the validity of our approach addressing the problem of the random walk process, pointing out a strong departure of the behavior observed in quenched real scale-free networks from the mean-field predictions. Additionally, we show how to employ our formalism for more complex dynamics. Our work sheds light on mean-field theory on weighted networks and on its range of validity, and warns about the reliability of mean-field results for complex dynamics.