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k-core percolation on multiplex networks.

N Azimi-Tafreshi1, J Gómez-Gardeñes2, S N Dorogovtsev3

  • 1Physics Department, Institute for Advanced Studies in Basic Sciences, 45195-1159 Zanjan, Iran.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2014
PubMed
Summary
This summary is machine-generated.

We introduce k-core percolation theory for multiplex networks, analyzing network structure across multiple interaction types. This research reveals hybrid phase transitions in these complex systems.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Multiplex networks consist of nodes connected by multiple types of edges, representing diverse interactions.
  • The k-core is a fundamental concept in network analysis, identifying densely connected subgraphs.
  • Generalizing k-core theory to multiplex networks is crucial for understanding complex systems with layered interactions.

Purpose of the Study:

  • To generalize the theory of k-core percolation to multiplex networks with M types of edges.
  • To derive self-consistency equations for k-core birth points and sizes in uncorrelated multiplex networks.
  • To investigate phase transitions and apply the k-core decomposition to real-world networks.

Main Methods:

  • Generalization of k-core theory to multiplex networks with degree vector k≡(k(1),k(2),...,k(M)).
  • Derivation of self-consistency equations for calculating k-core properties.
  • Analysis of uncorrelated multiplex networks with arbitrary degree distributions.
  • Specific solutions for two-layer Erdős-Rényi and scale-free multiplex networks.

Main Results:

  • Formulation of k-core theory for multiplex networks, defining the k-core based on minimum degree across all edge types.
  • Derivation of equations predicting the emergence and size of k-cores.
  • Identification of hybrid phase transitions at k-core emergence points, except for the (1,1)-core which exhibits a continuous transition.
  • Application of the k-core decomposition algorithm to air-transportation networks.

Conclusions:

  • The study provides a theoretical framework for k-core percolation on multiplex networks.
  • The findings reveal distinct phase transition behaviors depending on the k-core definition.
  • The k-core decomposition is a valuable tool for analyzing the structure of real-world multilayered systems like air-transportation networks.