Dynamics of diffusion on monoplex and multiplex networks: A message-passing approach

TL;DR

This paper introduces a message-passing approach to accurately model diffusion processes on complex networks, including multiplex networks, outperforming traditional mean-field methods by closely matching observed dynamics and identifying Nash equilibria.

Contribution

The paper develops a general message-passing framework for diffusion on complex and multiplex networks, providing more precise predictions than mean-field approximations.

Findings

Message-passing accurately replicates diffusion dynamics on synthetic networks.

Fixed points of the message-passing equations correspond to Nash equilibria.

Mean-field methods tend to overestimate diffusion size and frequency.

Abstract

New ideas and technologies adopted by a small number of individuals occasionally spread globally through a complex web of social ties. Here, we present a simple and general approximation method, namely, a message-passing approach, that allows us to describe the diffusion processes on complex networks in an almost exact manner. We consider two classes of binary-action games in each of which the best pure strategy for individual players is characterized as a variant of the threshold rule. We show that the dynamics of diffusion observed on synthetic networks are accurately replicated by the message-passing equation, whose fixed point corresponds to a Nash equilibrium. In contrast, the mean-field method tends to overestimate the size and frequency of diffusion. We extend the framework to analyze multiplex networks in which social interactions take place in multiple layers.