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JUMPn: A Streamlined Application for Protein Co-Expression Clustering and Network Analysis in Proteomics
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JUMPn: A Streamlined Application for Protein Co-Expression Clustering and Network Analysis in Proteomics

Published on: October 19, 2021

Bootstrap percolation on complex networks.

G J Baxter1, S N Dorogovtsev, A V Goltsev

  • 1Departamento de Física, I3N, Universidade de Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal. gjbaxter@ua.pt

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

Bootstrap percolation on complex networks shows continuous and discontinuous transitions. The giant active component is robust to damage in networks with diverging degree distributions.

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Last Updated: Jun 8, 2026

JUMPn: A Streamlined Application for Protein Co-Expression Clustering and Network Analysis in Proteomics
07:28

JUMPn: A Streamlined Application for Protein Co-Expression Clustering and Network Analysis in Proteomics

Published on: October 19, 2021

Area of Science:

  • Statistical Physics
  • Network Science
  • Complex Systems

Background:

  • Bootstrap percolation is a dynamical process on graphs.
  • Understanding its behavior on complex networks is crucial for various applications.
  • Previous studies have explored percolation on specific network types.

Purpose of the Study:

  • To investigate bootstrap percolation on uncorrelated complex networks.
  • To determine the phase diagram of the process concerning initial activation fraction (f) and undamaged vertex fraction (p).
  • To analyze the nature of transitions and the impact of network degree distribution.

Main Methods:

  • Simulation of bootstrap percolation on uncorrelated complex networks.
  • Analysis of phase transitions by varying parameters f and p.
  • Examination of network degree distributions, particularly those with a diverging second moment.

Main Results:

  • Identified two transitions: a continuous emergence of the giant active component and a potential second, discontinuous, hybrid transition.
  • Observed diverging avalanche sizes near the second critical point.
  • Discovered a special critical point where the second transition first emerges.
  • Found qualitatively different behavior in networks with diverging second moments in their degree distributions, leading to a robust giant active component for any f>0 and p>0 and absence of the discontinuous transition.

Conclusions:

  • The behavior of bootstrap percolation is highly dependent on network structure and parameters.
  • Networks with diverging second moments in degree distributions exhibit enhanced robustness and ease of activation for the giant active component.
  • A generalized bootstrap process with arbitrary vertex thresholds can be formulated.