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Weighted percolation on directed networks.

Juan G Restrepo1, Edward Ott, Brian R Hunt

  • 1Northeastern University, Boston, Massachusetts 02115, USA. juanga@neu.edu

Physical Review Letters
|March 21, 2008
PubMed
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This study analyzes network disintegration using node removal strategies in directed networks. A network breaks apart when the largest eigenvalue of a modified adjacency matrix falls below 1, offering a new theoretical framework.

Area of Science:

  • Network science
  • Graph theory
  • Statistical physics

Background:

  • Percolation transitions are critical phenomena in network science.
  • Understanding network robustness against node removal is crucial.
  • Existing models often rely on specific network properties or Markov models.

Purpose of the Study:

  • To develop a general theory for percolation transitions in directed networks.
  • To analyze the impact of general node removal strategies.
  • To provide a framework applicable beyond Markov network models.

Main Methods:

  • Heuristic arguments to predict network disintegration.
  • Analysis of the largest eigenvalue of a modified adjacency matrix.
  • Numerical testing of the proposed theoretical framework.

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Main Results:

  • A condition for network disintegration based on node removal probability p(i).
  • The critical condition is linked to the largest eigenvalue of A(ij)(1-p(i)) being less than 1.
  • The theory is validated through numerical tests.

Conclusions:

  • The proposed theory offers a novel criterion for network disintegration.
  • This approach is broadly applicable to locally treelike directed networks.
  • The method bypasses the need for Markov network models, expanding applicability.