The new challenges of multiplex networks: measures and models

TL;DR

This paper reviews the emerging field of multiplex networks, highlighting new measures and models that capture the complex interactions across multiple types of relationships in systems like society, the Internet, and the brain.

Contribution

It provides a comprehensive overview of structural measures and models for multiplex networks, emphasizing their importance in understanding complex systems.

Findings

Multiplexity causes significant qualitative and quantitative differences in system behaviors.

Various measures have been proposed to characterize multiplex network structures.

Models have been developed to reproduce and analyze multiplex network properties.

Abstract

What do societies, the Internet, and the human brain have in common? They are all examples of complex relational systems, whose emerging behaviours are largely determined by the non-trivial networks of interactions among their constituents, namely individuals, computers, or neurons, rather than the properties of the units themselves. In the last two decades, network scientists have proposed models of increasing complexity to better understand real-world systems. Only recently we have realised that multiplexity, i.e. the coexistence of several types of interactions among the constituents of a complex system, is responsible for substantial qualitative and quantitative differences in the type and variety of behaviours that a complex system can exhibit. As a consequence, multilayer and multiplex networks have become a hot topic in complexity science. Here we provide an overview of some of the measures proposed so far to characterise the structure of multiplex networks, and a selection of models aiming at reproducing those structural properties and quantifying their statistical significance. Focusing on a subset of relevant topics, this brief review is a quite comprehensive introduction to the most basic tools for the analysis of multiplex networks observed in the real-world. The wide applicability of multiplex networks as a framework to model complex systems in different fields, from biology to social sciences, and the colloquial tone of the paper will make it an interesting read for researchers working on both theoretical and experimental analysis of networked systems.