Percolation in real multiplex networks

TL;DR

This paper introduces an exact mathematical framework for analyzing site-percolation transitions in real multiplex networks, improving prediction accuracy over previous methods and confirming their robustness against random node removal.

Contribution

The authors develop a locally treelike ansatz-based approach to accurately describe percolation in sparse multiplex networks, validated across social, biological, and transportation systems.

Findings

Improved prediction of percolation diagrams in real multiplex networks

Confirmation of the robustness of multiplex networks against random node removal

The method outperforms previous approaches in accuracy

Abstract

We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where nodes are present in the system with given probability. The approach relies on the locally treelike ansatz, so that it is expected to accurately reproduce the true percolation diagram of sparse multiplex networks with negligible number of short loops. The performance of our theory is tested in social, biological, and transportation multiplex graphs. When compared against previously introduced methods, we observe improvements in the prediction of the percolation diagrams in all networks analyzed. Results from our method confirm previous claims about the robustness of real multiplex networks, in the sense that the average connectedness of the system does not exhibit any significant abrupt change as its individual components are randomly destroyed.