k-core structure of real multiplex networks

TL;DR

This paper investigates how inter-layer correlations influence the k-core structure of real multiplex networks, revealing that degree heterogeneity and node similarities play key roles in network robustness and organization.

Contribution

It demonstrates the importance of inter-layer correlations in shaping the k-core structure of multiplex networks, using novel control techniques and synthetic models.

Findings

Strong k-core structures are predicted by positive degree-degree correlations in heterogeneous networks.

In homogeneous networks, positive node similarity correlations lead to strong k-core structures.

Inter-layer correlations significantly impact network robustness and spreading processes.

Abstract

Multiplex networks are convenient mathematical representations for many real-world -- biological, social, and technological -- systems of interacting elements, where pairwise interactions among elements have different flavors. Previous studies pointed out that real-world multiplex networks display significant inter-layer correlations -- degree-degree correlation, edge overlap, node similarities -- able to make them robust against random and targeted failures of their individual components. Here, we show that inter-layer correlations are important also in the characterization of their $\mathbf{k}$-core structure, namely the organization in shells of nodes with increasingly high degree. Understanding $k$-core structures is important in the study of spreading processes taking place on networks, as for example in the identification of influential spreaders and the emergence of localization phenomena. We find that, if the degree distribution of the network is heterogeneous, then a strong $\mathbf{k}$-core structure is well predicted by significantly positive degree-degree correlations. However, if the network degree distribution is homogeneous, then strong $\mathbf{k}$-core structure is due to positive correlations at the level of node similarities. We reach our conclusions by analyzing different real-world multiplex networks, introducing novel techniques for controlling inter-layer correlations of networks without changing their structure, and taking advantage of synthetic network models with tunable levels of inter-layer correlations.