Link overlap, viability, and mutual percolation in multiplex networks

TL;DR

This paper explores how link overlap influences the viability and mutual percolation in multiplex networks, revealing its significant role in network robustness and the complexity it introduces to analytical modeling.

Contribution

It provides a comprehensive analytical and numerical investigation of link overlap effects on multiplex network viability, clarifies existing controversies, and highlights the complex behaviors induced by overlap.

Findings

Link overlap greatly enhances network viability and mutual percolation.

Presence of link overlap leads to diverse hysteretic behaviors in viability.

Overlapping links respond differently to removal strategies, affecting network robustness.

Abstract

Many real-world complex systems are best modeled by multiplex networks. The multiplexity has proved to have broad impact on the system's structure and function. Most theoretical studies on multiplex networks to date, however, have largely ignored the effect of link overlap across layers despite strong empirical evidences for its significance. In this article, we investigate the effect of link overlap in the viability of multiplex networks, both analytically and numerically. Distinctive role of overlapping links in viability and mutual connectivity is emphasized and exploited for setting up proper analytic framework. A rich phase diagram for viability is obtained and greatly diversified patterns of hysteretic behavior in viability are observed in the presence of link overlap. Mutual percolation with link overlap is revisited as a limit of multiplex viability problem, and controversy between existing results is clarified. The distinctive role of overlapping links is further demonstrated by the different responses of networks under random removals of overlapping and non-overlapping links, respectively, as well as under several removal strategies. Our results show that the link overlap strongly facilitates viability and mutual percolation; at the same time, the presence of link overlap poses challenge in analytical approach to the problem.