Weighted percolation on directed networks.

@article{Restrepo2008WeightedPO,
  title={Weighted percolation on directed networks.},
  author={Juan G. Restrepo and Edward Ott and Brian R. Hunt},
  journal={Physical review letters},
  year={2008},
  volume={100 5},
  pages={058701}
}
We present and numerically test an analysis of the percolation transition for general node removal strategies valid for locally treelike directed networks. On the basis of heuristic arguments we predict that, if the probability of removing node i is p(i), the network disintegrates if p(i) is such that the largest eigenvalue of the matrix with entries A(ij)(1-p(i)) is less than 1, where A is the adjacency matrix of the network. The knowledge or applicability of a Markov network model is not… CONTINUE READING
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