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Weighted evolving networks.

S H Yook1, H Jeong, A L Barabási

  • 1Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA.

Physical Review Letters
|June 21, 2001
PubMed
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This study introduces evolving network models with weighted links, moving beyond binary interactions. Results show weighted network distributions asymptotically match connectivity distributions, despite logarithmic corrections.

Area of Science:

  • Complex systems science
  • Network theory
  • Statistical physics

Background:

  • Many real-world systems (biological, ecological, economic) are complex networks with varying interaction strengths.
  • Existing network evolution models are often binary, lacking nuanced representation of interaction intensity.

Purpose of the Study:

  • To introduce and analyze evolving network models incorporating weighted links.
  • To investigate the scaling properties of these weighted evolving networks.
  • To understand how link weights affect network structure and dynamics.

Main Methods:

  • Development of a novel class of weighted evolving network models.
  • Combined analytical and numerical approaches to study network properties.
  • Analysis of scaling behavior and distribution convergence.

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Main Results:

  • The total weight distribution in evolving weighted networks exhibits asymptotic convergence to the connectivity distribution.
  • Strong logarithmic corrections were identified, influencing the convergence rate.
  • The models provide a more realistic framework for studying complex systems.

Conclusions:

  • Weighted evolving network models offer a more accurate representation of real-world systems.
  • Understanding scaling properties and corrections is crucial for network analysis.
  • This work advances the study of complex systems by incorporating link heterogeneity.