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Related Experiment Videos

Scale-free networks are ultrasmall.

Reuven Cohen1, Shlomo Havlin

  • 1Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan, Israel. cohenr@shoshi.ph.biu.ac.il

Physical Review Letters
|March 14, 2003
PubMed
Summary

Scale-free networks exhibit smaller diameters than random networks. For specific degree distributions (2

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Area of Science:

  • Network science
  • Statistical physics

Background:

  • Scale-free networks are characterized by a power-law degree distribution p(k) ∝ k^(-lambda).
  • The diameter (mean distance between nodes) is a crucial network metric.

Purpose of the Study:

  • To analytically determine the diameter of scale-free networks.
  • To compare network diameter scaling with regular and small-world networks.

Main Methods:

  • Analytical arguments were employed to derive network diameter.
  • The study considered scale-free networks with N sites and varying exponent lambda.

Main Results:

  • For 2
  • For lambda=3, diameter scales as d ∝ ln(N)/ln(ln(N).
  • For lambda>3, diameter scales as d ∝ ln(N).

Conclusions:

  • Scale-free networks with 2
  • Deterministic scale-free networks can achieve the minimal possible diameter of d ∝ ln(ln(N).