Diffusion Dynamics and Optimal Coupling in Directed Multiplex Networks

TL;DR

This paper investigates how diffusion processes behave on directed multiplex networks, revealing that an intermediate level of coupling can optimize diffusion speed, with implications for complex systems.

Contribution

It introduces the concept of optimal coupling in directed multiplex networks and demonstrates its effects through simple models and real-world data.

Findings

Optimal diffusion occurs at intermediate coupling levels.

Directed multiplex networks can outperform fully coupled networks in diffusion speed.

Real-world topology confirms the existence of optimal coupling regimes.

Abstract

We study the dynamics of diffusion processes acting on directed multiplex networks, i.e., coupled multilayer networks where at least one layer consists of a directed graph. We reveal that directed multiplex networks may exhibit a faster diffusion at an intermediate degree of coupling than when the two layers are fully coupled. We use three simple multiplex examples and a real-world topology to illustrate the characteristics of the directed dynamics that give rise to a regime in which an optimal coupling exists. Given the ubiquity of both directed and multilayer networks in nature, our results could have important implications for the dynamics of multilevel complex systems towards optimality.