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Resilience of the internet to random breakdowns
Cohen1, Erez, ben-Avraham
1Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.
Physical Review Letters
|November 18, 2000
Summary
Large network stability against random node removal is analyzed. Scale-free networks are remarkably robust, requiring over 99% of nodes to be removed before disintegration.
Area of Science:
- Network Science
- Statistical Physics
Background:
- Many large-scale networks, such as the Internet, exhibit scale-free connectivity following a power-law distribution P(k) = ck(-alpha).
- Understanding network resilience to random node failures is crucial for infrastructure stability.
Purpose of the Study:
- To investigate the stability of scale-free networks against random site removal using percolation theory.
- To derive a general condition for network disintegration based on the critical fraction of removed nodes.
Main Methods:
- Application of percolation theory to model network stability.
- Analytical and numerical studies to determine critical thresholds for network collapse.
- Analysis of power-law degree distributions, specifically P(k) = ck(-alpha).
Main Results:
- For scale-free networks with alpha <= 3, disintegration does not occur unless the network is finite.
- The critical fraction of nodes (p(c)) required for network collapse was determined.
- The Internet's physical structure (alpha approximately 2.5) demonstrates exceptional robustness, with p(c) > 0.99.
Conclusions:
- Scale-free networks possess inherent resilience to random failures, particularly those with lower alpha values.
- The Internet's structure is highly robust, indicating a high tolerance for random node loss.
- Percolation theory provides a powerful framework for assessing the stability of complex networks.