The new challenges of multiplex networks: Measures and models

What do societies, the Internet, and the human brain have in common?They are all examples of complex relational systems, whose emergingbehaviours are largely determined by the non-trivial networks ofinteractions among their constituents, namely individuals, computers, orneurons, rather than only by the properties of the units themselves. Inthe last two decades, network scientists have proposed models ofincreasing complexity to better understand real-world systems. Onlyrecently we have realised that multiplexity, i.e. the coexistence ofseveral types of interactions among the constituents of a complexsystem, is responsible for substantial qualitative and quantitativedifferences in the type and variety of behaviours that a complex systemcan exhibit. As a consequence, multilayer and multiplex networks havebecome a hot topic in complexity science. Here we provide an overview ofsome of the measures proposed so far to characterise the structure ofmultiplex networks, and a selection of models aiming at reproducingthose structural properties and quantifying their statisticalsignificance. Focusing on a subset of relevant topics, this brief reviewis a quite comprehensive introduction to the most basic tools for theanalysis of multiplex networks observed in the real-world. The wideapplicability of multiplex networks as a framework to model complexsystems in different fields, from biology to social sciences, and thecolloquial tone of the paper will make it an interesting read forresearchers working on both theoretical and experimental analysis ofnetworked systems.