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Giant components in directed multiplex networks.

N Azimi-Tafreshi1, S N Dorogovtsev2, J F F Mendes3

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

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2014
PubMed
Summary
This summary is machine-generated.

Giant components in directed multiplex networks generalize the bow-tie structure. For m edge types, 3^m giant components exist, including a strongly viable component, with sizes estimated for uncorrelated networks.

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Area of Science:

  • Network Science
  • Complex Systems
  • Graph Theory

Background:

  • Traditional directed networks exhibit a bow-tie structure for giant components.
  • Multiplex networks possess multiple edge types, adding complexity.
  • Understanding giant components is crucial for network analysis.

Purpose of the Study:

  • To generalize the bow-tie structure to directed multiplex networks.
  • To identify and characterize different types of giant components.
  • To determine the number and size of these components, especially the strongly viable component.

Main Methods:

  • Defining giant components based on directed paths of specific edge types.
  • Introducing the concept of a strongly viable component for m=2 edge types.
  • Analyzing uncorrelated directed multiplex networks to estimate component sizes.

Main Results:

  • Directed multiplex networks contain 3^m distinct giant components.
  • A strongly viable component is identified for m=2 edge types.
  • Exact size and emergence point of the strongly viable component are derived.
  • Sizes of other giant components are estimated for uncorrelated networks.

Conclusions:

  • The bow-tie structure is generalized to directed multiplex networks.
  • A rich landscape of giant components exists in multiplex networks.
  • The framework provides insights into the global structure of complex multilayered systems.