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.