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Weak Multiplex Percolation

Weak Multiplex Percolation

$20.00 (P)

Part of Elements in Structure and Dynamics of Complex Networks

  • Publication planned for: January 2022
  • availability: Not yet published - available from January 2022
  • format: Paperback
  • isbn: 9781108791076

$ 20.00 (P)
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  • 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.

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    Product details

    • Publication planned for: January 2022
    • format: Paperback
    • isbn: 9781108791076
    • dimensions: 229 x 152 mm
    • availability: Not yet published - available from January 2022
  • Table of Contents

    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.

  • Authors

    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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