More is different in real-world multilayer networks

The constituents of many complex systems are characterized by non-trivial connectivity patterns and dynamical processes that are well captured by network models. However, most systems are coupled with each other through interdependencies, characterized by relationships among heterogeneous units, or multiplexity, characterized by the coexistence of different kinds of relationships among homogeneous units. Multilayer networks provide the framework to capture the complexity typical of systems of systems, enabling the analysis of biophysical, social and human-made networks from an integrated perspective. Here I review the most important theoretical developments in the past decade, showing how the layered structure of multilayer networks is responsible for phenomena that cannot be observed from the analysis of subsystems in isolation or from their aggregation, including enhanced diffusion, emergent mesoscale organization and phase transitions. I discuss applications spanning multiple spatial scales, from the cell to the human brain and to ecological and social systems, and offer perspectives and challenges on future research directions.Describing interdependencies and coupling between complex systems requires tools beyond what the framework of single networks offers. This Review covers recent developments in the study and modelling of multilayer networks.