K-core structure of real multiplex networks

Saeed Osat,Fragkiskos Papadopoulos,Filippo Radicchi

doi:10.1103/physrevresearch.2.023176

Abstract

The authors show that interlayer correlations are responsible for the strong k-core structure found in real world multiplex networks. The more heterogeneous are the degree distributions of the layers, the more pivotal is the role of degree correlations. The less heterogeneous are the degree distributions, the more crucial is the role of correlations at the level of node similarities. These findings may help in identifying influential spreaders in real world multiplex systems.

Highlights

A multiplex network is a collection of single-layer networks sharing common nodes, where each layer captures a different type of pairwise interaction among nodes [1,2,3,4,5]
While the core organization of single-layer networks has been extensively studied in the past, little is known about the core organization of real multiplex networks
We performed a systematic characterization of the k-core structure of real-world multiplex networks, and shown that real multiplex networks possess a strong k-core structure that is due to interlayer correlations

Summary

INTRODUCTION

A multiplex network is a collection of single-layer networks sharing common nodes, where each layer captures a different type of pairwise interaction among nodes [1,2,3,4,5]. In many real-world networks, the notion of maximal k-core, i.e., the core with the largest k, represents a good structural proxy for the understanding of dynamical localization phenomena in spreading processes [30]. [32], Azimi-Tafreshi and collaborators studied the emergence of k-cores in random uncorrelated multiplex network models with arbitrary degree distributions They showed that k-cores in multiplex networks are characterized by abrupt transitions, but their properties cannot be deduced from those of the k-cores of the individual network layers. Geometric correlations can be quantified either for radial or angular coordinates of the nodes Both types of correlations are able to provide insights about the k-core structure of a multiplex. These observations are in remarkable agreement with the behavior observed in synthetic multiplex networks where we can control the level of geometric correlations across the layers [23]

Single-layer networks

Hyperbolic embedding

Multiplex networks

DISCUSSION AND CONCLUSION

S1 model

Geometric multiplex model