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Hierarchical scale-free network is fragile against random failure
Takehisa Hasegawa1, Koji Nemoto2
1Graduate School of Information Science, Tohoku University, 6-3-09, Aramaki-Aza-Aoba, Sendai, Miyagi 980-8579, Japan.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 4, 2014
Summary
Site percolation in hierarchical scale-free networks shows a threshold of 1, indicating fragility. This network is highly susceptible to random failures and intentional attacks, unlike bond percolation.
Area of Science:
- Network Science
- Statistical Physics
- Complex Systems
Background:
- Hierarchical scale-free networks exhibit complex structures.
- Percolation theory studies connectivity in networks.
- The Dorogovtsev-Goltsev-Mendes network is a model for such systems.
Purpose of the Study:
- To investigate site percolation thresholds in the Dorogovtsev-Goltsev-Mendes network.
- To compare site percolation with bond percolation in this network.
- To assess the network's robustness against random failures and intentional attacks.
Main Methods:
- Utilizing the generating function method.
- Analyzing site percolation dynamics.
- Comparing results with bond percolation thresholds.
Main Results:
- The site percolation threshold for the Dorogovtsev-Goltsev-Mendes network is found to be 1.
- The network is not in a percolating phase for occupation probabilities less than 1.
- The percolation threshold for intentional attacks is also 1, contrasting with zero for bond percolation.
Conclusions:
- The hierarchical scale-free network is highly fragile to both random failures and intentional attacks.
- This fragility stems from its inherent hierarchical structure.
- Such structural vulnerabilities are common in hierarchical network models.
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