Percolation in self-similar networks

Details Percolation in self-similar networks Percolation in self-similar networks

2010-10-27

arxiv.org/abs/1010.5793v2

Phys. Rev. Lett. 106, 048701 (2011)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.106.048701

We provide a simple proof that graphs in a general class of self-similar networks have zero percolation threshold. The considered self-similar networks include random scale-free graphs with given expected node degrees and zero clustering, scale-free graphs with finite clustering and metric structure, growing scale-free networks, and many real networks. The proof and the derivation of the giant component size do not require the assumption that networks are treelike. Our results rely only on the observation that self-similar networks possess a hierarchy of nested subgraphs whose average degree grows with their depth in the hierarchy. We conjecture that this property is pivotal for percolation in networks.

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