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Generalized percolation in random directed networks.

Marián Boguñá1, M Angeles Serrano

  • 1Departament de Física Fonamental, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
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We present a new theory for percolation in directed random networks, incorporating bidirectional edges and correlations. This framework predicts percolation thresholds and giant component sizes, validated by simulations.

Area of Science:

  • Network science
  • Statistical physics
  • Complex systems

Background:

  • Percolation theory traditionally studies simple network structures.
  • Directed networks and edge correlations are crucial for realistic models.
  • Bidirectional edges introduce unique dynamics not captured by standard models.

Purpose of the Study:

  • To develop a general theory for percolation in directed random networks.
  • To incorporate arbitrary two-point correlations and bidirectional edges.
  • To derive equations for critical thresholds and component sizes.

Main Methods:

  • Development of a general mathematical framework for percolation.
  • Derivation of analytical equations for percolation threshold.
  • Derivation of analytical equations for giant component size.

Related Experiment Videos

  • Computational simulations for validation.

    • Main Results:

    • A generalized theory for percolation in directed networks with correlations and bidirectional edges.
    • Derived equations for percolation threshold and giant component size.
    • Simulation results confirm theoretical predictions for uncorrelated networks with bidirectional edges.

    Conclusions:

    • The inclusion of bidirectional edges and correlations significantly alters percolation phenomena.
    • The developed theory provides a robust framework for analyzing complex network structures.
    • This work offers new perspectives on understanding connectivity in directed systems.