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Area of Science:

  • Network Science
  • Statistical Physics
  • Computer Science

Background:

  • K-core decomposition is a key tool for empirical network analysis.
  • Existing theoretical models have limitations in capturing complex network structures.

Purpose of the Study:

  • To integrate k-core decomposition into a theoretical network model.
  • To develop a hard-core random network (HRN) model for generating networks with specific degree and k-core properties.
  • To analyze the bond percolation problem on these networks.

Main Methods:

  • Introduction of the hard-core random network (HRN) model.
  • Exact solution of the bond percolation problem on the HRN model.
  • Analytical estimation of network properties.
  • Comparison with real-world network databases.

Main Results:

  • The HRN model generates maximally random networks with specified degree distributions and k-core structures.
  • Fast and precise analytical estimates for bond percolation were obtained.
  • The HRN model demonstrated superior performance compared to existing models.

Conclusions:

  • The proposed HRN model provides a robust theoretical framework for complex network analysis.
  • Explicit integration of k-core structure enhances network modeling capabilities.
  • The approach offers improved accuracy and efficiency for network analysis.