Weak percolation on multiplex networks.
Bootstrap percolation is a simple but nontrivial 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.
Department of Physics & I3N, University of Aveiro, Portugal.
Gareth J
GJ
Baxter
Department of Physics & I3N, University of Aveiro, Portugal and A. F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia.
Sergey N
SN
Dorogovtsev
Department of Physics & I3N, University of Aveiro, Portugal.
José F F
JF
Mendes
MACSI, Department of Mathematics and Statistics, University of Limerick, Ireland.
Davide
D
Cellai