Weighted percolation on directed networks

Details Weighted percolation on directed networks Weighted percolation on directed networks

2007-04-04

arxiv.org/abs/0704.0491v1

Physics

Condensed Matter

Soft Condensed Matter

4 pages, 2 figures

Scientific paper

10.1103/PhysRevLett.100.058701

We present an analysis of the percolation transition for general node removal strategies valid for locally tree-like 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 required by our theory, thus making it applicable to situations not covered by previous works. We test our predicted percolation criterion against numerical results for different networks and node removal strategies.

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