Spectral properties of the Laplacian of multiplex networks

TL;DR

This paper extends the spectral analysis of the Laplacian in multiplex networks, providing analytical tools to understand how interconnections influence diffusion and synchronization phenomena.

Contribution

It introduces a decoupling framework for the Laplacian spectrum in multiplex networks, enabling analytical expressions for eigenvalues and insights into dynamical processes.

Findings

Derived analytical expressions for the Laplacian spectrum

Unraveled the role of interconnections in diffusion and synchronization

Provided a decoupling approach for multiplex spectral analysis

Abstract

One of the more challenging tasks in the understanding of dynamical properties of models on top of complex networks is to capture the precise role of multiplex topologies. In a recent paper, Gomez et al. [Phys. Rev. Lett. 101, 028701 (2013)] proposed a framework for the study of diffusion processes in such networks. Here, we extend the previous framework to deal with general configurations in several layers of networks, and analyze the behavior of the spectrum of the Laplacian of the full multiplex. We derive an interesting decoupling of the problem that allow us to unravel the role played by the interconnections of the multiplex in the dynamical processes on top of them. Capitalizing on this decoupling we perform an asymptotic analysis that allow us to derive analytical expressions for the full spectrum of eigenvalues. This spectrum is used to gain insight into physical phenomena on top of multiplex, specifically, diffusion processes and synchronizability.