Diffusion geometry of multiplex and interdependent systems

TL;DR

This paper extends the concept of diffusion geometry to multilayer networks, analyzing how various random walk dynamics reveal the underlying geometric structure of complex interconnected systems across different domains.

Contribution

It introduces a framework for diffusion geometry in multilayer networks using diverse random walk dynamics, overcoming previous limitations and applying it to real-world systems.

Findings

Multilayer diffusion geometry captures complex network structures.

Different random walk dynamics influence the geometric features.

Application to empirical systems reveals insights into system organization.

Abstract

Complex networks are characterized by latent geometries induced by their topology or by the dynamics on the top of them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by adequate metrics. Random walks, a proxy for a broad spectrum of processes, from simple contagion to metastable synchronization and consensus, have been recently used in [Phys. Rev. Lett. 118, 168301 (2017)] to define the class of diffusion geometry and pinpoint the functional mesoscale organization of complex networks from a genuine geometric perspective. Here, we firstly extend this class to families of distinct random walk dynamics -- including local and nonlocal information -- on multilayer networks -- a paradigm for biological, neural, social, transportation, biological and financial systems -- overcoming limitations such as the presence of isolated nodes and disconnected components, typical of real-world networks. Secondly, we characterize the multilayer diffusion geometry of synthetic and empirical systems, highlighting the role played by different random search dynamics in shaping the geometric features of the corresponding diffusion manifolds.