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k-core (bootstrap) percolation on complex networks: critical phenomena and nonlocal effects
A V Goltsev1, S N Dorogovtsev, J F F Mendes
1Departamento de Física da Universidade de Aveiro, Portugal.
Summary
We introduce bootstrap percolation theory for k-cores on random networks. This hybrid phase transition shows unique critical phenomena driven by the k-core
Area of Science:
- Network Science
- Statistical Physics
- Phase Transitions
Background:
- K-core percolation is a fundamental concept in network analysis.
- Understanding phase transitions in random networks is crucial for complex systems.
Purpose of the Study:
- To develop the theory of k-core (bootstrap) percolation on uncorrelated random networks.
- To analyze the hybrid phase transition and critical phenomena associated with k-core percolation.
Main Methods:
- Developing theoretical framework for k-core percolation on random networks.
- Analyzing the role of the k-core corona in percolation dynamics.
- Mapping k-core percolation to a cooperative relaxation model.
Main Results:
- Identified k-core percolation as a hybrid phase transition (first-order jump and continuous singularity).
- Demonstrated the critical role of the k-core corona and its clusters.
- Established a connection between k-core percolation and cooperative relaxation dynamics.
Conclusions:
- The k-core corona's percolation threshold dictates the overall transition.
- The mean separation of corona clusters acts as a diverging correlation length.
- K-core percolation exhibits critical relaxation phenomena analogous to cooperative models.
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