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Uncorrelated random networks.

Z Burda1, A Krzywicki

  • 1Fakultät für Physik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 6, 2003
PubMed
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This study introduces a method for generating nondegenerate graphs, finding that scale-free networks require internode correlations for accurate modeling, regardless of the specific network model used.

Area of Science:

  • Statistical physics
  • Network science
  • Graph theory

Background:

  • Previous work considered trees and degenerate graphs.
  • This study focuses on nondegenerate graphs (no multiple or self-connections).
  • Node degrees are arbitrary, but nodes are uncorrelated.

Purpose of the Study:

  • To define and generate a statistical ensemble of nondegenerate graphs.
  • To investigate finite-size effects in scale-free graphs.
  • To determine the necessity of internode correlations in scale-free network physics.

Main Methods:

  • Development of an efficient algorithm for generating nondegenerate graphs.
  • Analysis of finite-size effects in scale-free networks with arbitrary degree distributions.
  • Mathematical derivation of degree distribution cutoff in uncorrelated scale-free graphs.

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Main Results:

  • An efficient algorithm for generating nondegenerate graphs is presented.
  • The degree distribution in uncorrelated scale-free graphs is found to be cut off at a specific degree value.
  • The cutoff scales with the number of nodes N as N(gamma), where gamma=min[1/2, 1/(beta-1)].

Conclusions:

  • Internode correlations are a necessary component in the physics of real-world scale-free networks.
  • The findings hold independently of specific network models.
  • This research complements earlier studies on graph ensembles.