A unified approach to percolation processes on multiplex networks

TL;DR

This paper develops a unified framework for understanding percolation processes on multiplex networks, revealing how different definitions of connectivity affect the system's resilience and transition types.

Contribution

It introduces two definitions of percolation on multiplex networks, analyzing their impact on the nature of phase transitions and system robustness.

Findings

Strong non-local rule causes abrupt collapse of giant component

Weak local rule allows both continuous and discontinuous transitions

Different percolation definitions lead to varied resilience behaviors

Abstract

Many real complex systems cannot be represented by a single network, but due to multiple sub-systems and types of interactions, must be represented as a multiplex network. This is a set of nodes which exist in several layers, with each layer having its own kind of edges, represented by different colours. An important fundamental structural feature of networks is their resilience to damage, the percolation transition. Generalisation of these concepts to multiplex networks requires careful definition of what we mean by connected clusters. We consider two different definitions. One, a rigorous generalisation of the single-layer definition leads to a strong non-local rule, and results in a dramatic change in the response of the system to damage. The giant component collapses discontinuously in a hybrid transition characterised by avalanches of diverging mean size. We also consider another definition, which imposes weaker conditions on percolation and allows local calculation, and also leads to different sized giant components depending on whether we consider an activation or pruning process. This 'weak' process exhibits both continuous and discontinuous transitions.