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Weak percolation on multiplex networks.

Gareth J Baxter1, Sergey N Dorogovtsev2, José F F Mendes1

  • 1Department of Physics & I3N, University of Aveiro, Portugal.

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|May 16, 2014
PubMed
Summary
This summary is machine-generated.

We introduce weak percolation models for multiplex networks, distinguishing bootstrap and pruning percolation. These models reveal new critical phenomena and have applications in contagion processes and network diagnostics.

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Area of Science:

  • Complex Systems
  • Network Science
  • Statistical Physics

Background:

  • Bootstrap percolation is a fundamental model on random networks with broad scientific applications.
  • In single-layer networks, bootstrap percolation is the inverse of pruning percolation.
  • Multiplex networks, composed of multiple interconnected layers, present unique challenges for percolation models.

Purpose of the Study:

  • To propose and analyze models of bootstrap and pruning percolation specifically for multiplex networks.
  • To introduce the concept of "weak" percolation, differentiating it from ordinary ("strong") percolation.
  • To explore the novel critical phenomena arising from the decoupling of bootstrap and pruning percolation in multiplexes.

Main Methods:

  • Development of distinct bootstrap and pruning percolation models tailored for multiplex network structures.
  • Analytical framework to calculate critical behavior and characterize critical clusters within these models.
  • Comparison of model behavior in simplex versus multiplex networks to highlight decoupling effects.

Main Results:

  • Bootstrap and pruning percolation models, unified in simplex networks, exhibit distinct behaviors in multiplex networks.
  • The proposed models reveal a rich landscape of critical phenomena unique to multiplex percolation.
  • The bootstrap model serves as a foundational contagion process model for multiplex networks.

Conclusions:

  • Weak percolation models offer a new perspective on network dynamics in multiplex systems.
  • The bootstrap percolation model has potential applications in areas like critical infrastructure recovery and information security.
  • The pruning percolation model may serve as a tool for identifying missing layers in multiplex networks.