Bootstrap percolation and the geometry of complex networks

Research output: Contribution to journalArticle

Authors

Colleges, School and Institutes

External organisations

  • University of Warwick, Warwick, United Kingdom.

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 infected neighbors becomes infected, remaining so forever.We identify a function p_c(N)=o(1) such that a.a.s. when p >> p_c(N) the infection spreads to a positive fraction of vertices, whereas when p << p_c(N) the process cannot evolve. Moreover, this behavior is ``robust'' under random deletions of edges.

Details

Original languageEnglish
Pages (from-to)234-264
Number of pages30
JournalStochastic Processes and their Applications
Volume126
Issue number1
Early online date31 Aug 2015
Publication statusPublished - 31 Aug 2015

Keywords

  • bootstrap percolation, robustness, random hyperbolic graphs, Hyperbolic plane