Bond percolation on multiplex networks

TL;DR

This paper develops an analytical method for bond percolation on multiplex networks, revealing new phase transition phenomena and assessing the benefits of multilayer modeling over monoplex projections.

Contribution

It introduces a novel analytical framework for bond percolation in multiplex networks and uncovers new critical phenomena not observed in monoplex networks.

Findings

Analytical predictions match monoplex results in many cases.

Discovery of multiple percolation phase transitions in certain multiplex networks.

Application to transportation datasets demonstrates real-world relevance.

Abstract

We present an analytical approach for bond percolation on multiplex networks and use it to determine the expected size of the giant connected component and the value of the critical bond occupation probability in these networks. We advocate the relevance of these tools to the modeling of multilayer robustness and contribute to the debate on whether any benefit is to be yielded from studying a full multiplex structure as opposed to its monoplex projection, especially in the seemingly irrelevant case of a bond occupation probability that does not depend on the layer. Although we find that in many cases the predictions of our theory for multiplex networks coincide with previously derived results for monoplex networks, we also uncover the remarkable result that for a certain class of multiplex networks, well described by our theory, new critical phenomena occur as multiple percolation phase transitions are present. We provide an instance of this phenomenon in a multipex network constructed from London rail and European air transportation datasets.