Unique superdiffusion induced by directionality in multiplex networks

TL;DR

This paper reveals that directionality in multilayer networks can induce a novel superdiffusion regime, where diffusion surpasses the speed of undirected systems, highlighting the importance of considering directed interactions in complex systems.

Contribution

The study introduces a framework for analyzing diffusive dynamics in directed multilayer networks and demonstrates how directionality can cause superdiffusion, a phenomenon not observed in undirected systems.

Findings

Directionality causes non-monotonic diffusion behavior.

Superdiffusion occurs at intermediate interlayer coupling.

Superdiffusion depends on layer directionality and topological overlap.

Abstract

The multilayer network framework has served to describe and uncover a number of novel and unforeseen physical behaviors and regimes in interacting complex systems. However, the majority of existing studies are built on undirected multilayer networks while most complex systems in nature exhibit directed interactions. Here, we propose a framework to analyze diffusive dynamics on multilayer networks consisting of at least one directed layer. We rigorously demonstrate that directionality in multilayer networks can fundamentally change the behavior of diffusive dynamics: from monotonic (in undirected systems) to non-monotonic diffusion with respect to the interlayer coupling strength. Moreover, for certain multilayer network configurations, the directionality can induce a unique superdiffusion regime for intermediate values of the interlayer coupling, wherein the diffusion is even faster than that corresponding to the theoretical limit for undirected systems, i.e., the diffusion in the integrated network obtained from the aggregation of each layer. We theoretically and numerically show that the existence of superdiffusion is fully determined by the directionality of each layer and the topological overlap between layers. We further provide a formulation of multilayer networks displaying superdiffusion. Our results highlight the significance of incorporating the interacting directionality in multilevel networked systems and provide a framework to analyze dynamical processes on interconnected complex systems with directionality.