Correlated Edge Overlaps in Multiplex Networks

TL;DR

This paper develops a theoretical framework for analyzing sparse multiplex networks with overlapping links, revealing how correlations influence phase transitions and the structure of the giant mutually connected component.

Contribution

It introduces a novel theory for multiplex networks with correlated overlapping links, enabling analysis of phase transitions and connectivity properties.

Findings

Correlations significantly alter the phase diagram.

Multiple hybrid phase transitions occur due to correlations.

Assortative correlations lead to recurrent hybrid phase transitions.

Abstract

We develop the theory of sparse multiplex networks with partially overlapping links based on their local tree-likeness. This theory enables us to find the giant mutually connected component in a two-layer multiplex network with arbitrary correlations between connections of different types. We find that correlations between the overlapping and non-overlapping links markedly change the phase diagram of the system, leading to multiple hybrid phase transitions. For assortative correlations we observe recurrent hybrid phase transitions.