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Bootstrap percolation and the geometry of complex networks

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  • Candellero, Elisabetta
  • Fountoulakis, Nikolaos

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.

Suggested Citation

  • Candellero, Elisabetta & Fountoulakis, Nikolaos, 2016. "Bootstrap percolation and the geometry of complex networks," Stochastic Processes and their Applications, Elsevier, vol. 126(1), pages 234-264.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:1:p:234-264
    DOI: 10.1016/j.spa.2015.08.005
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    Cited by:

    1. Mitsche, Dieter & Pérez-Giménez, Xavier & Prałat, Paweł, 2017. "Strong-majority bootstrap percolation on regular graphs with low dissemination threshold," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 3110-3134.
    2. Tian, Xu & Geng, Yong & Sarkis, Joseph & Gao, Cuixia & Sun, Xin & Micic, Tatyana & Hao, Han & Wang, Xin, 2021. "Features of critical resource trade networks of lithium-ion batteries," Resources Policy, Elsevier, vol. 73(C).
    3. Komjáthy, Júlia & Lodewijks, Bas, 2020. "Explosion in weighted hyperbolic random graphs and geometric inhomogeneous random graphs," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1309-1367.

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