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Percolation transitions in scale-free networks under the Achlioptas process
1Center for Theoretical Physics and Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea.
Physical Review Letters
|November 13, 2009
Summary
The Achlioptas process (AP) can cause discontinuous percolation transitions in scale-free networks. However, a continuous transition is also possible, depending on the network
Area of Science:
- Network Science
- Statistical Physics
Background:
- Percolation transitions in Erdos-Rényi networks and square lattices under the Achlioptas process (AP) are typically discontinuous.
- Scale-free networks exhibit high structural heterogeneity due to the presence of hubs.
Purpose of the Study:
- To investigate the nature of percolation transitions in heterogeneous scale-free networks under the Achlioptas process.
- To determine if a continuous transition is possible and identify the factors influencing it.
Main Methods:
- Analysis of percolation transitions in scale-free networks with varying degree distributions under the Achlioptas process.
- Investigating the interplay between the Achlioptas process and network hubs.
Main Results:
- Discontinuous percolation transitions are not guaranteed in heterogeneous scale-free networks under the Achlioptas process.
- A continuous transition is possible and depends on the specific degree distribution of the scale-free network.
- The competition between the Achlioptas process and network hubs dictates the transition type.
Conclusions:
- The heterogeneity of scale-free networks can alter the percolation transition dynamics.
- The degree distribution plays a crucial role in determining whether a continuous or discontinuous transition occurs.
- Further research is needed to fully characterize the transition behavior and estimate critical exponents.
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