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Related Experiment Videos

Growing scale-free networks with tunable clustering.

Petter Holme1, Beom Jun Kim

  • 1Department of Theoretical Physics, Umeå University, 901 87 Umeå, Sweden. holme@tp.umu.se

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 28, 2002
PubMed
Summary

We introduce a triad formation step to scale-free networks, enhancing clustering while maintaining power-law distributions and small average geodesic lengths. This model offers tunable clustering via a simple control parameter.

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Area of Science:

  • Network Science
  • Complex Systems
  • Graph Theory

Background:

  • Scale-free networks are fundamental models in network science.
  • Standard models often lack high clustering coefficients.
  • Real-world networks frequently exhibit both scale-free properties and high clustering.

Purpose of the Study:

  • To extend the standard scale-free network model.
  • To incorporate a triad formation step to increase network clustering.
  • To analyze the geometric properties of the modified network model.

Main Methods:

  • Analytical calculations.
  • Numerical simulations.
  • Extension of the standard scale-free network model with a triad formation step.

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Main Results:

  • The proposed model retains the power-law degree distribution characteristic of scale-free networks.
  • The model achieves a small average geodesic length, similar to standard scale-free networks.
  • High clustering coefficients are achieved, and the clustering coefficient is tunable via a control parameter.

Conclusions:

  • The extended model successfully integrates high clustering with scale-free properties.
  • The triad formation step provides a mechanism to control network clustering.
  • This model offers a more realistic representation of certain real-world complex networks.