Escaping the avalanche collapse in self-similar multiplexes

TL;DR

This paper explores how self-similarity and interlayer degree correlations influence the robustness and stability of multiplex networks, revealing conditions under which they become fragile or resilient to failures.

Contribution

It introduces the concept of self-similarity in multiplexes and demonstrates how interlayer degree correlations can drastically alter their stability properties.

Findings

Self-similarity explains multiplex fragility and robustness.

Interlayer degree correlations can eliminate the percolation threshold.

Numerical simulations confirm theoretical predictions.

Abstract

We deduce and discuss the implications of self-similarity for the stability in terms of robustness to failure of multiplexes, depending on interlayer degree correlations. First, we define self-similarity of multiplexes and we illustrate the concept in practice using the configuration model ensemble. Circumscribing robustness to survival of the mutually percolated state, we find a new explanation based on self-similarity both for the observed fragility of interconnected systems of networks and for their robustness to failure when interlayer degree correlations are present. Extending the self-similarity arguments, we show that interlayer degree correlations can change completely the stability properties of self-similar multiplexes, so that they can even recover a zero percolation threshold and a continuous transition in the thermodynamic limit, qualitatively exhibiting thus the ordinary stability attributes of noninteracting networks. We confirm these results with numerical simulations.