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Heterogeneous K-core percolation on hypergraphs.

Dandan Zhao¹, Wenjia Xi¹, Bo Zhang^2,3

¹School of Computer Science and Technology, Zhejiang Normal University, Jinhua 321004, Zhejiang, China.

Chaos (Woodbury, N.Y.)

|March 27, 2025

Summary

This summary is machine-generated.

This study introduces a hyperedge K-core percolation model for complex systems, revealing that heterogeneity parameters significantly impact network robustness and phase transitions under attacks.

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Area of Science:

Complex Systems Science
Network Science
Statistical Physics

Background:

Complex systems exhibit interactions described by hypergraphs.
K-core percolation analyzes system robustness against attacks, but lacks hypergraph theoretical studies on node heterogeneity.

Purpose of the Study:

To develop a hyperedge K-core percolation model for hypergraphs incorporating heterogeneity.
To investigate the impact of heterogeneity parameters on network robustness and phase transitions.

Main Methods:

Constructed a hyperedge K-core percolation model with heterogeneity parameters.
Mapped random hypergraphs to factor graphs to analyze the giant connected component and percolation threshold.
Conducted extensive simulation experiments to validate theoretical findings.

Main Results:

Theoretical predictions closely matched simulation results.
Heterogeneity parameters significantly influence the giant connected component magnitude and phase transition type.
Decreasing heterogeneity increases network fragility; increasing it enhances resilience.

Conclusions:

The proposed model effectively captures the impact of heterogeneity on hypergraph robustness.
Heterogeneity parameters offer a tunable mechanism to control network resilience against cascading failures.
A decrease in heterogeneity can lead to a hybrid phase transition, altering network behavior.