Weak percolation on multiplex networks
This work addresses percolation theory for multiplex networks, with potential applications in critical infrastructure recovery and information security, but it appears incremental as it extends existing simplex network models to multiplexes.
The authors tackled the problem of modeling percolation processes on multiplex networks by proposing bootstrap and pruning percolation models, collectively termed 'weak' percolation, and showed that these models decouple in multiplexes, leading to diverse critical phenomena.
Bootstrap percolation is a simple but non-trivial model. It has applications in many areas of science and has been explored on random networks for several decades. In single layer (simplex) networks, it has been recently observed that bootstrap percolation, which is defined as an incremental process, can be seen as the opposite of pruning percolation, where nodes are removed according to a connectivity rule. Here we propose models of both bootstrap and pruning percolation for multiplex networks. We collectively refer to these two models with the concept of "weak" percolation, to distinguish them from the somewhat classical concept of ordinary ("strong") percolation. While the two models coincide in simplex networks, we show that they decouple when considering multiplexes, giving rise to a wealth of critical phenomena. Our bootstrap model constitutes the simplest example of a contagion process on a multiplex network and has potential applications in critical infrastructure recovery and information security. Moreover, we show that our pruning percolation model may provide a way to diagnose missing layers in a multiplex network. Finally, our analytical approach allows us to calculate critical behavior and characterize critical clusters.