Multilayer Networks

Abstract

Multilayer networks are formed by several networks that interact with each other and co-evolve. Multilayer networks include social networks, financial markets, transportation systems, infrastructures and molecular networks and the brain. The multilayer structure of these networks strongly affects the properties of dynamical and stochastic processes defined on them, which can display unexpected characteristics. For example, interdependencies between different networks of a multilayer structure can cause cascades of failure events that can dramatically increase the fragility of these systems; spreading of diseases, opinions and ideas might take advantage of multilayer network topology and spread even when its single layers cannot sustain an epidemic when taken in isolation; diffusion on multilayer transportation networks can significantly speed up with respect to diffusion on single layers; finally, the interplay between multiplexity and controllability of multilayer networks is a problem with major consequences in financial, transportation, molecular biology and brain networks. This field is one of the most prosperous recent developments of Network Science and Data Science. Multilayer networks include multiplex networks, multi-slice temporal networks, networks of networks, interdependent networks. Multilayer networks are characterized by having a highly correlated multilayer network structure, providing a significant advantage for extracting information from them using multilayer network measures and centralities and community detection methods. The multilayer network dynamics (including percolation, epidemic spreading, diffusion, synchronization, game theory and control) is strongly affected by the multilayer network topology. This book will present a comprehensive account of this emerging field.

Spreading of localized attacks on spatial multiplex networks with a community structure

“…This interdependence can cause a spread of damages, and lead to a cascade of failures and even entire system collapse. Therefore, many studies have been carried out to analyze cascading failures in interdependent networks [1][2][3][4][5][6][7][8][9][10][11]. Many of these studies have focused on the multiplex network model, which is an important example of an interdependent network where the same nodes are linked by different layers [12][13][14][15].…”

Diffusion processes in multilayer transportation networks: the flight of the Coronavirus

“…A multiplex network is a particular case of a multilayer network with the following properties [11] Because in a multiplex network, there is no explicit treatment of interlinks, it can be viewed as:…”

“…As we mentioned before, we are interested in the propagation of the current outbreak of coronavirus SARS-CoV-2. Diffusion of any kind, such as diseases, in a network is a fundamental dynamic process described by the transport of a continuous quantity along its edges [11]. There are several ways of modeling diffusion in a network, such as SIR and SIS models [12,13], nevertheless, one of the simplest forms is with a random walk model.…”

Fragility of a multilayer network of intranational supply chains

“…Different approaches have been employed to model diffusion processes in multilayer networks (Aleta and Moreno 2019 ; Bianconi 2018 ; Boccaletti et al 2014 ; Kivelä et al 2014 ). Several authors have performed comprehensive reviews of these approaches (Bródka et al 2020 ; de Arruda et al 2018 ; De Domenico et al 2016 ; Kivelä et al 2014 ; Salehi et al 2015 ), therefore we do not review them here.…”