On degree-degree correlations in multilayer networks

TL;DR

This paper introduces a tensor-based approach to measure degree-degree correlations in multilayer networks, revealing that analyzing layers separately can lead to different insights than considering the interconnected system, especially for disease spreading.

Contribution

It generalizes assortativity measures to multilayer networks using tensor representation, applicable to weighted networks and considering inter-layer correlations.

Findings

Contrasting results when analyzing layers independently versus interconnected.

Degree correlations significantly affect disease spreading dynamics.

The approach applies to weighted and multilayer networks.

Abstract

We propose a generalization of the concept of assortativity based on the tensorial representation of multilayer networks, covering the definitions given in terms of Pearson and Spearman coefficients. Our approach can also be applied to weighted networks and provides information about correlations considering pairs of layers. By analyzing the multilayer representation of the airport transportation network, we show that contrasting results are obtained when the layers are analyzed independently or as an interconnected system. Finally, we study the impact of the level of assortativity and heterogeneity between layers on the spreading of diseases. Our results highlight the need of studying degree-degree correlations on multilayer systems, instead of on aggregated networks.