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Emergence of biconnected clusters in explosive percolation.
1School of Physics, <a href="https://ror.org/02czkny70">Hefei University of Technology</a>, Hefei, Anhui 230009, China.
Physical Review. E
|August 20, 2024
Summary
Explosive percolation shows a sharp phase transition. This study reveals that while biconnected clusters share the same percolation threshold, their fractal dimension and size distribution vary with bond competition rules.
Area of Science:
- Complex systems
- Statistical physics
- Network science
Background:
- Explosive percolation (EP) is a network model exhibiting a sharp phase transition.
- High-order connectivity, specifically biconnectivity, is crucial for understanding network robustness.
- Previous studies focused on simple connectivity, leaving higher-order structures underexplored.
Purpose of the Study:
- Investigate high-order connectivity in explosive percolation.
- Analyze the role of intracluster bond competition on biconnected clusters.
- Determine the universality and scaling properties of biconnected clusters in EP.
Main Methods:
- Utilized an event-based ensemble simulation approach.
- Focused on analyzing biconnected clusters (pairs of nodes connected by at least two independent paths).
- Examined variations in intracluster bond competition rules.
Main Results:
- Confirmed that biconnected clusters percolate simultaneously with simply connected clusters across different competition rules.
- Demonstrated that the volume fractal dimension (d_f') of biconnected clusters is dependent on intracluster bond competition rules.
- Observed double-scaling behavior in the size distribution of biconnected clusters, with distinct scaling for large and small clusters.
Conclusions:
- Explosive percolation's universality holds for biconnected clusters, irrespective of intracluster bond competition.
- Intracluster bond competition significantly influences the geometric properties (fractal dimension) and size distribution of biconnected clusters.
- The findings highlight complex scaling behaviors and provide deeper insights into network connectivity in explosive percolation models.
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