Weak Multiplex Percolation

This Element describes a generalisation of percolation to multilayer networks: weak multiplex percolation, where a node belongs to a connected component if at least one of its neighbours in each layer is in this component. In two layers with finite second moments of the degree distributions, the authors observe an unusual continuous transition with quadratic growth above the threshold. In three or more layers, the authors find a discontinuous hybrid transition which persists even in highly heterogeneous degree distributions, becoming continuous only when the powerlaw exponent reaches $1+1/(M-1)$ for $M$ layers.

Format: Paperback / softback
Length: 75 pages
Publication date: 27 January 2022
Publisher: Cambridge University Press

In numerous systems composed of interconnected subsystems, the intricate interplay between elements can be accurately depicted through the utilization of multilayer networks. Nevertheless, the fundamental concept of percolation, which plays a crucial role in comprehending connectivity and robustness, presents a challenge when extended to multiple layers. This Element introduces a novel generalization of percolation to multilayer networks: weak multiplex percolation. A node is considered part of a connected component if at least one of its neighbors in each layer is also a member of that component. The authors meticulously detail the critical phenomena associated with this process. When examining two layers with finite second moments of the degree distributions, the authors observe an extraordinary continuous transition characterized by quadratic growth above a certain threshold. However, when the second moments diverge, the singularity is determined by the asymptotics of the degree distributions, resulting in a diverse range of critical behaviors. In three or more layers, the authors encounter a discontinuous hybrid transition that persists even in highly heterogeneous degree distributions. This transition becomes continuous only when the powerlaw exponent reaches $1+1/(M-1)$ for $M$ layers.

Weight: 92g
Dimension: 151 x 230 x 7 (mm)
ISBN-13: 9781108791076
Edition number: New ed