Bootstrap percolation and the geometry of complex networks

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Candellero, Elisabetta¹  Fountoulakis, Nikolaos² 

[1] Univ Warwick, Dept Stat, Coventry CV4 7AL, W Midlands, England

[2] Univ Birmingham, Sch Math, Birmingham B15 2TT, W Midlands, England

关键词: Random geometric graph;    Hyperbolic plane;    Bootstrap percolation;    Percolation;   

DOI  :  10.1016/j.spa.2015.08.005

来源: Elsevier

【 摘 要 】

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 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. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free