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Convergence towards an Erdős-Rényi graph structure in network contraction processes
Ido Tishby1, Ofer Biham1, Eytan Katzav1
1Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel.
Physical Review. E
|October 24, 2019
Summary
Network contraction processes, driven by node deletions, transform scale-free networks into Erdős-Rényi structures. This evolution leads to a decreasing mean degree and loss of correlations in complex networks.
Area of Science:
- Network Science
- Statistical Physics
- Complex Systems
Background:
- Networks often exhibit scale-free structures due to growth processes with preferential attachment.
- Real-world networks face contraction phases from node failures, attacks, or epidemics.
- Understanding network evolution under contraction is crucial for system resilience.
Purpose of the Study:
- To analyze the structural evolution of networks during contraction processes.
- To investigate the impact of different node deletion strategies (random, preferential, propagating) on network structure.
- To determine the final network state after contraction.
Main Methods:
- Utilized master equation formulation for theoretical analysis.
- Employed computer simulations to model network contraction.
- Analyzed degree distributions and degree-degree correlations.
Main Results:
- Contracting networks converge towards an Erdős-Rényi network structure.
- The mean degree of the network decreases as contraction progresses.
- Degree distributions shift towards a Poisson distribution, and degree-degree correlations are lost.
Conclusions:
- Network contraction fundamentally alters network topology, moving away from scale-free properties.
- The final state is characterized by random connections and reduced heterogeneity.
- These findings have implications for understanding network stability and robustness.
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