Weak multiplex percolation / Gareth J. Baxte [and three others].

Format:

Book

Author/Creator:

Baxter, Gareth J., author.

Series:

Cambridge elements. Elements in structure and dynamics of complex networks 2516-5763

Language:

English

Subjects (All):

Percolation (Statistical physics).

Physical Description:

1 online resource (40 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2021.

Summary:

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.

Contents:

Cover

Title Page

Copyright Page

Weak Multiplex Percolation

Contents

1 Introduction

2 Weak Multiplex Percolation

2.1 Self-Consistency Equations for Weak Multiplex Percolation

3 Relation to Other Percolation Models

3.1 Percolation in a Single-Layer Network

3.2 The Mutually Connected Component in Multilayer Networks

4 Critical Phenomena with Rapidly Decaying Degree Distributions

4.1 Two Layers

4.2 Three or More Layers

4.2.1 Avalanches

5 Critical Phenomena with Broad Degree Distributions

5.1 Two Layers

5.1.1 Non-symmetric Layers

5.2 More Than Two Layers

5.2.1 Non-symmetric Layers

6 Conclusions

Appendix A

Effect of Edge Removal on Degree Distributions

Appendix B

Generating Functions

References

Acknowledgements.

Notes:

Title from publisher's bibliographic system (viewed on 22 Dec 2021).

ISBN:

9781108857499

1108857493

9781108865777

1108865771

OCLC:

1492942592