Article,
Weighted Percolation on Directed Networks
Physical Review Letters, 100 (5): 058701+ (February 2008)
DOI: 10.1103/physrevlett.100.058701
Abstract
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 pi, the network disintegrates if pi is such that the largest eigenvalue of the matrix with entries Aij(1-pi) 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.
