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Percolation transition in networks with degree-degree correlation
1Department of Physics, University of Seoul, Seoul 130-743, Korea.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 13, 2007
Summary
We developed a network model to study how degree correlations affect percolation. Positive correlations alter percolation transitions, suggesting they explain unusual behavior in growing network models.
Area of Science:
- Network Science
- Statistical Physics
Background:
- Percolation transitions are critical phenomena in network analysis.
- Understanding how network structure, specifically degree correlations, influences these transitions is crucial.
Purpose of the Study:
- To introduce an exponential random graph model with tunable degree-degree correlations.
- To investigate the impact of positive and negative degree correlations on percolation transitions in networks with a fixed Poisson degree distribution.
Main Methods:
- Developed an exponential random graph model.
- Analyzed percolation transitions in networks with varying degree correlations.
- Characterized critical phenomena using cluster size distributions and scaling laws.
Main Results:
- Negative degree correlations (disassortative networks) do not change the universality class of the percolation transition compared to uncorrelated networks.
- Positive degree correlations (assortative networks) are relevant, significantly altering the percolation transition.
- Assortative networks exhibit a unique percolation transition with non-diverging mean finite cluster sizes and power-law scalings.
Conclusions:
- The nature of percolation transitions is strongly influenced by positive degree-degree correlations.
- Assortative degree correlations may explain the distinct percolation behaviors observed in growing network models.
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