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Related Experiment Video

Updated: Jan 20, 2026

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Eradicating abrupt collapse on single network with dependency groups.

Jiarong Xie1, Youyou Yuan1, Zhengping Fan1

  • 1School of Data and Computer Science, Sun Yat-sen University, Guangzhou 510006, China.

Chaos (Woodbury, N.Y.)
|September 2, 2019
PubMed
Summary
This summary is machine-generated.

Preventing catastrophic cascades in grouped single-layer networks is achievable by reinforcing a constant density of nodes. This finding applies to various network types, offering insights into designing resilient infrastructure.

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Area of Science:

  • Network Science
  • Complex Systems
  • Infrastructure Resilience

Background:

  • Cascading failures are critical in complex networks.
  • Existing research focuses on multilayered networks, neglecting single-layer grouped networks.
  • Catastrophic cascades in dependent grouped networks require specific prevention strategies.

Purpose of the Study:

  • To investigate methods for preventing catastrophic cascades in single-layer grouped networks.
  • To determine the optimal node reinforcement density for network resilience.
  • To analyze the impact of group dependency on network stability.

Main Methods:

  • Analytical solutions derived for dependent Erdős-Rényi (ER), random regular (RR), and scale-free (SF) networks.
  • Node reinforcement density calculated for various network structures and group sizes.
  • Phase transition behaviors analyzed across different network models.

Main Results:

  • Randomly reinforcing a constant density of nodes effectively prevents catastrophic collapses.
  • An analytical solution for the required reinforced node density was found.
  • A constant reinforcement density of 0.1756 is sufficient for ER (group size 2), RR, and SF networks.
  • Hybrid phase transition behavior observed in RR and SF networks, but not ER networks.

Conclusions:

  • Random node reinforcement is a viable strategy for enhancing the resilience of grouped single-layer networks.
  • The findings provide a universal density for preventing catastrophic cascades in several network types.
  • Understanding network topology and group dependencies is crucial for infrastructure design.