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Percolation in directed scale-free networks.

N Schwartz1, R Cohen, D Ben-Avraham

  • 1Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
PubMed
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This study explores percolation in directed scale-free networks. We identified three distinct regimes with unique percolation exponents, revealing how network structure impacts resilience.

Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Complex networks in nature often exhibit directed links, influencing network navigability and topology.
  • Understanding percolation properties in these directed networks is crucial for various scientific domains.

Purpose of the Study:

  • To investigate the percolation properties of directed scale-free networks with correlated degree distributions.
  • To derive a phase diagram characterizing different percolation regimes and their exponents.

Main Methods:

  • Analysis of directed scale-free networks with correlated in- and out-degree distributions.
  • Derivation of a phase diagram based on degree exponents.
  • Analytical calculation of anomalous exponents in specific regimes.

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Main Results:

  • Identification of three distinct percolation regimes in directed scale-free networks.
  • Regime 1 recovers known directed percolation mean-field exponents.
  • Regimes 2 and 3 exhibit anomalous exponents, with Regime 3 showing resilience to dilution (percolation threshold approaching 1).

Conclusions:

  • The study provides a comprehensive phase diagram for percolation in directed scale-free networks.
  • Anomalous scaling behaviors and enhanced resilience are identified in specific network configurations.
  • Findings offer insights into the structural robustness and navigability of complex directed systems.