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Renormalization group for evolving networks.

S N Dorogovtsev1

  • 1AF Ioffe Physico-Technical Institute, 194021 St Petersburg, Russia. sdorogov@fc.up.pt

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 6, 2003
PubMed
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We developed a renormalization group method for stochastically growing networks. This analysis reveals that percolation on growing scale-free networks exhibits different critical behavior compared to uncorrelated networks.

Area of Science:

  • Statistical Physics
  • Network Science
  • Complex Systems

Background:

  • Stochastic network growth is a key factor in many real-world systems.
  • Understanding phase transitions in dynamic networks is crucial.
  • Previous studies often assumed static or uncorrelated network structures.

Purpose of the Study:

  • To introduce a renormalization group (RG) framework for analyzing stochastically growing networks.
  • To investigate the critical behavior of percolation on growing scale-free networks.
  • To compare the findings with existing models of uncorrelated networks.

Main Methods:

  • A real-space renormalization group approach was applied.
  • The study focused on percolation processes.
  • The network model incorporated stochastic growth and scale-free properties.

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Main Results:

  • The renormalization group treatment successfully models growing networks.
  • Percolation on growing scale-free networks shows distinct critical behavior.
  • This behavior deviates from that observed in uncorrelated network models.

Conclusions:

  • The proposed RG method provides a novel way to study dynamic network phenomena.
  • Stochastic growth significantly alters the critical properties of networks.
  • The findings highlight the importance of considering network evolution in analyses.