Multilayer networks: metrics and spectral properties

Multilayer networks represent systems in which there are several topological levels each one representing one kind of interaction or interdependency between the systems’ elements. These networks have attracted a lot of attention recently because their study allows considering different dynamical modes concurrently. Here, we revise the main concepts and tools developed up to date. Specifically, we focus on several metrics for multilayer network characterization as well as on the spectral properties of the system, which ultimately enable for the dynamical characterization of several critical phenomena. The theoretical framework is also applied for description of real-world multilayer systems. Emanuele Cozzo Institute for Biocomputation and Physics of Complex Systems (BIFI) and Department of Theoretical Physics, University of Zaragoza, 50018 Zaragoza, Spain, e-mail: [email protected] Guilherme Ferraz de Arruda Departamento de Matemática Aplicada e Estatı́stica, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos, SP, Brazil. e-mail: [email protected] Francisco A. Rodrigues Departamento de Matemática Aplicada e Estatı́stica, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos, SP, Brazil. e-mail: [email protected] Yamir Moreno Institute for Biocomputation and Physics of Complex Systems (BIFI) and Department of Theoretical Physics, University of Zaragoza, 50018 Zaragoza, Spain and Complex Networks and Systems Lagrange Lab, Institute for Scientific Interchange, Turin, Italy e-mail: yamir.moreno@gmail. com 1 ar X iv :1 50 4. 05 56 7v 1 [ ph ys ic s. so cph ] 2 1 A pr 2 01 5 2 Authors Suppressed Due to Excessive Length