Correlated multiplexity and connectivity of multiplex random networks

TL;DR

This paper investigates how correlated multiplexity influences the connectivity and giant component formation in multiplex random networks, revealing that correlation patterns can drastically alter network connectivity thresholds.

Contribution

It introduces a simple model of multiplex random networks demonstrating the significant impact of correlated multiplexity on network connectivity and giant component emergence.

Findings

Maximal correlation leads to giant components at any nonzero link density.

Maximal anti-correlation delays giant component formation but results in full network connectivity at finite link density.

Imperfect correlated multiplexity cases are also discussed.

Abstract

Nodes in a complex networked system often engage in more than one type of interactions among them; they form a multiplex network with multiple types of links. In real-world complex systems, a node's degree for one type of links and that for the other are not randomly distributed but correlated, which we term correlated multiplexity. In this paper we study a simple model of multiplex random networks and demonstrate that the correlated multiplexity can drastically affect the properties of giant component in the network. Specifically, when the degrees of a node for different interactions in a duplex Erdos-Renyi network are maximally correlated, the network contains the giant component for any nonzero link densities. In contrast, when the degrees of a node are maximally anti-correlated, the emergence of giant component is significantly delayed, yet the entire network becomes connected into a single component at a finite link density. We also discuss the mixing patterns and the cases with imperfect correlated multiplexity.