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Scale-free networks from self-organization.

T S Evans1, J P Saramäki

  • 1Theoretical Physics, Blackett Laboratory, Imperial College London, Prince Consort Road, London, SW7 2BW, UK. t.evans@imperial.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2005
PubMed
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Scale-free networks naturally emerge from growing networks using random walks for vertex selection. This self-organizing process, based on local information, accurately predicts network growth and can generate weighted networks.

Area of Science:

  • Network Science
  • Complex Systems
  • Statistical Physics

Background:

  • Understanding the emergence of scale-free degree distributions in growing networks is crucial for modeling complex systems.
  • Existing models often rely on global information or specific preferential attachment rules.

Purpose of the Study:

  • To demonstrate a novel mechanism for generating scale-free degree distributions in growing networks.
  • To explore the self-organizing properties of network growth based on local information.
  • To generalize the method for creating weighted networks with power-law distributions.

Main Methods:

  • Utilizing random walks on networks to select vertices for new attachments.
  • Employing local graph information exclusively for the network growth process.

Related Experiment Videos

  • Comparing analytical results from mean-field equations with simulated network data.

    • Main Results:

    • Scale-free degree distributions naturally emerge from the random walk-based growth mechanism across various parameters.
    • The self-organizing process is well-approximated by standard mean-field equations.
    • The random walk algorithm was successfully generalized to produce weighted networks with power-law distributions of weight and degree.

    Conclusions:

    • Random walks provide a natural and self-organizing mechanism for generating scale-free networks.
    • This approach offers a robust method for network growth modeling and weighted network construction.