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Random graphs with arbitrary clustering and their applications.

Peter Mann1,2, V Anne Smith1,2, John B O Mitchell1,2

  • 1School of Computer Science, University of St Andrews, St. Andrews, Fife KY16 9SX, United Kingdom.

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Summary
This summary is machine-generated.

This study extends network analysis to complex networks with non-equivalent node clustering, improving characterization of bond percolation properties in real-world systems.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Real-world networks often exhibit complex structures that are not locally treelike.
  • Existing network analysis methods struggle to accurately characterize bond percolation properties in such non-treelike networks.
  • Previous work provided analytical solutions for homogeneous clustering, but a gap exists for heterogeneous clustering.

Purpose of the Study:

  • To extend analytical solutions for bond percolation properties to complex networks with heterogeneous clustering.
  • To investigate the percolation behavior of multilayer networks with non-degree-equivalent nodes.
  • To provide a more versatile framework for analyzing random complex networks with arbitrary clustering.

Main Methods:

  • Development of analytical solutions for percolation properties in networks with non-degree-equivalent clusters.
  • Extension of the configuration model and generating function formulation to accommodate arbitrary clustering.
  • Numerical simulations to validate the extended model and demonstrate its applicability.

Main Results:

  • The proposed method successfully characterizes bond percolation properties in networks with heterogeneous clustering.
  • The model is applicable to multilayer networks and other complex structures.
  • Numerical examples confirm the accuracy and extended applicability of the analytical solutions.

Conclusions:

  • The extended model significantly enhances the analysis of bond percolation in complex networks beyond homogeneous clustering.
  • This framework offers a powerful tool for understanding network properties in diverse real-world systems, including multilayer networks.
  • The findings extend the utility of established network models like the configuration model.