Bootstrap percolation and the geometry of complex networks

Elisabetta Candellero and Nikolaos Fountoulakis

Stochastic Processes and their Applications, 2016, vol. 126, issue 1, 234-264

Abstract: On a geometric model for complex networks (introduced by Krioukov et al.) we investigate the bootstrap percolation process. This model consists of random geometric graphs on the hyperbolic plane having N vertices, a dependent version of the Chung–Lu model. The process starts with infection rate p=p(N). Each uninfected vertex with at least r≥1 infected neighbors becomes infected, remaining so forever. We identify a function pc(N)=o(1) such that a.a.s. when p≫pc(N) the infection spreads to a positive fraction of vertices, whereas when p≪pc(N) the process cannot evolve. Moreover, this behavior is “robust” under random deletions of edges.

Keywords: Random geometric graph; Hyperbolic plane; Bootstrap percolation; Percolation (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:126:y:2016:i:1:p:234-264

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DOI: 10.1016/j.spa.2015.08.005

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