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Scaling and percolation in the small-world network model.

M E Newman1, D J Watts

  • 1Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
Summary

This study analyzes the Watts and Strogatz small-world network model, identifying a critical length-scale that governs network behavior and diverges at a critical point. This scale impacts disease propagation models and network dimensions.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • The Watts and Strogatz model captures key features of social interaction networks.
  • Understanding network properties like length-scale is crucial for modeling complex systems.

Purpose of the Study:

  • To investigate the critical length-scale in the small-world network model.
  • To analyze network behavior, including crossover phenomena and effective dimensions.
  • To model disease propagation using site percolation on these networks.

Main Methods:

  • Analytical derivation of critical exponents and finite size scaling.
  • Application of series expansion and Padé approximants.
  • Numerical simulations to validate theoretical findings.

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Main Results:

  • Identification of a nontrivial length-scale governing large- to small-world transitions.
  • Calculation of the effective dimension of small-world graphs, exhibiting multifractal-like behavior.
  • Derivation of an approximate expression for epidemic threshold in disease propagation models.

Conclusions:

  • The small-world network model exhibits a critical point and a characteristic length-scale.
  • Network dimension is scale-dependent, similar to multifractals.
  • Percolation analysis provides insights into disease spread dynamics on these networks.