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Mesoscopics and fluctuations in networks.

S N Dorogovtsev1, A N Samukhin

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

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 12, 2003
PubMed
Summary

We analyzed fluctuations in finite-size networks and found their degree distribution spectrum is Poissonian. These fluctuations are significant in networks with many connections and fat-tailed distributions.

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Area of Science:

  • Network Science
  • Statistical Physics

Background:

  • Understanding network properties is crucial for various scientific fields.
  • Finite-size networks exhibit complex connection patterns.

Purpose of the Study:

  • To investigate the nature of fluctuations in finite-size networks.
  • To characterize the degree distribution spectrum of these networks.

Main Methods:

  • Analysis of fluctuations in networks with complex connection distributions, P(k).
  • Examination of the spectrum of fluctuations for the number of vertices with a given degree.

Main Results:

  • The spectrum of fluctuations was found to be Poissonian.
  • Mesoscopic fluctuations are pronounced in the high-degree region (P(k) ~ 1/N).
  • These fluctuations are important in networks with fat-tailed degree distributions.

Conclusions:

  • The study characterizes fluctuations in finite-size networks.
  • Poissonian fluctuation spectrum is a key finding for networks with complex degree distributions.
  • The importance of mesoscopic fluctuations in fat-tailed networks is highlighted.

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