Percolation in self-similar networks

Abstract

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.

4 pages, 3 figures

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• Multiple phase transitions of the susceptible-infected-susceptible epidemic model on complex networks
• Detecting the ultra low dimensionality of real networks
• Clustering of random scale-free networks
• Emergence of geometric Turing patterns in complex networks
• Non-Markovian epidemic spreading on temporal networks
• A geometry-induced topological phase transition in random graphs
• Scaling of Clusters near Discontinuous Percolation Transitions in Hyperbolic Networks
• Spatial effects in real networks: measures, null models, and applications
• Scale-invariant geometric random graphs
• Network Renormalization
• Cosmological networks
• Dynamic Behavior of Interacting between Epidemics and Cascades on Heterogeneous Networks
• Manageable to unmanageable transition in a fractal model of project networks