Characterization of multiple topological scales in multiplex networks through supra-Laplacian eigengaps

Abstract

Multilayer networks have been the subject of intense research during the last few years, as they represent better the interdependent nature of many real world systems. Here, we address the question of describing the three different structural phases in which a multiplex network might exist. We show that each phase can be characterized by the presence of gaps in the spectrum of the supra-Laplacian of the multiplex network. We therefore unveil the existence of different topological scales in the system, whose relation characterizes each phase. Moreover, by capitalizing on the coarse-grained representation that is given in terms of quotient graphs, we explain the mechanisms that produce those gaps as well as their dynamical consequences.

6 pages and 4 Figures. Final version. To appear in PRE

References in corpus (5)

• Synchronization in complex networks
• Critical phenomena in complex networks
• Diffusion dynamics on multiplex networks
• Covariance, correlation matrix and the multi-scale community structure of networks
• Exact Coupling Threshold for Structural Transition in Interconnected Networks

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• Structural transition in interdependent networks with regular interconnections
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