Weak Multiplex Percolation

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Gareth J. Baxter (Universidade de Aveiro, Portugal) Rui A. da Costa (Universidade de Aveiro, Portugal)

Weak Multiplex Percolation

Gareth J. Baxter (Universidade de Aveiro, Portugal), Rui A. da Costa (Universidade de Aveiro, Portugal), Sergey N. Dorogovtsev (Universidade de Aveiro, Portugal) , José F. F. Mendes (Universidade de Aveiro, Portugal)

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English

Cambridge University Press
27 January 2022

Discrete mathematics; Statistical physics; Mathematical physics; Maths for computer scientists

Series: Elements in the Structure and Dynamics of Complex Networks

In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially generalised to multiple layers. This Element describes a generalisation of percolation to multilayer networks: weak multiplex percolation. A node belongs to a connected component if at least one of its neighbours in each layer is in this component. The authors fully describe the critical phenomena of this process. In two layers with finite second moments of the degree distributions the authors observe an unusual continuous transition with quadratic growth above the threshold. When the second moments diverge, the singularity is determined by the asymptotics of the degree distributions, creating a rich set of critical behaviours. 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.

By: Gareth J. Baxter (Universidade de Aveiro Portugal), Rui A. da Costa (Universidade de Aveiro, Portugal), Sergey N. Dorogovtsev (Universidade de Aveiro, Portugal), José F. F. Mendes (Universidade de Aveiro, Portugal)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Edition: New edition
Dimensions: Height: 228mm, Width: 151mm, Spine: 4mm
Weight: 93g
ISBN: 9781108791076
ISBN 10: 1108791077
Series: Elements in the Structure and Dynamics of Complex Networks
Pages: 75
Publication Date: 27 January 2022
Audience: General/trade , ELT Advanced
Format: Paperback
Publisher's Status: Active

1. Introduction; 2. Weak multiplex percolation; 3. Relation to other percolation models; 4. Critical phenomena with rapidly decaying degree distributions; 5. Critical phenomena with broad degree distributions; 6. Conclusions; References.