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Growing scale-free networks with small-world behavior.

Konstantin Klemm1, Víctor M Eguíluz

  • 1Center for Chaos and Turbulence Studies, Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark. klemm@nbi.dk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2002
PubMed
Summary

We present a dynamical model for growing networks that explains scale-free degree distribution and the small-world effect. This model yields a large clustering coefficient, independent of network size, unifying key network properties.

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Area of Science:

  • Network Science
  • Complex Systems
  • Dynamical Systems

Background:

  • Real-world networks exhibit complex topological features, including scale-free degree distributions and the small-world effect.
  • Understanding the underlying mechanisms that generate these properties in growing networks is crucial for network analysis.

Purpose of the Study:

  • To introduce a simple dynamical model that unifies scale-free degree distribution and the small-world effect in growing networks.
  • To analytically investigate the behavior of the clustering coefficient in relation to system size.

Main Methods:

  • Development of a simple dynamical model for network growth.
  • Derivation of analytical expressions for the clustering coefficient in limiting cases.

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Main Results:

  • The model successfully reproduces scale-free degree distribution and the small-world effect.
  • The average shortest path length increases logarithmically with system size.
  • A large clustering coefficient, independent of system size, was observed.

Conclusions:

  • The proposed dynamical model provides a unified framework for understanding key features of real-world networks.
  • Analytical expressions for the clustering coefficient were derived for random and highly clustered scale-free networks.