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Related Experiment Videos

Emergence of tempered preferential attachment from optimization.

Raissa M D'Souza1, Christian Borgs, Jennifer T Chayes

  • 1Department of Mechanical and Aeronautical Engineering, University of California, Davis, CA 95616, USA. raissa@cse.ucdavis.edu

Proceedings of the National Academy of Sciences of the United States of America
|March 31, 2007
PubMed
Summary

This study demonstrates how preferential attachment arises from optimization, introducing saturation and viability. This network model explains power-law distributions observed across diverse real-world systems.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Preferential attachment is a key mechanism in network growth, but its theoretical origins remain debated.
  • Existing models often fail to capture the full complexity of real-world network structures.

Purpose of the Study:

  • To resolve the theoretical controversy surrounding preferential attachment by embedding it within an optimization framework.
  • To introduce and analyze novel features of saturation and viability in preferential attachment models.
  • To develop generalized models that explain broad classes of power-law degree distributions with exponential cutoffs.

Main Methods:

  • Developing an optimization framework that naturally yields preferential attachment.
  • Introducing and mathematically defining saturation and viability parameters.
  • Generalizing the preferential attachment model to incorporate independent saturation and viability.
  • Empirically testing the model's predictions against diverse real-world network data.

Main Results:

  • Demonstrated that preferential attachment can emerge from an optimization process.
  • Identified saturation and viability as inherent properties of this optimized preferential attachment model.
  • Showed that the model generates power-law degree distributions with exponential cutoffs.
  • Validated the model's excellent fit to empirical data from social, biological, physical, and technological networks.

Conclusions:

  • Optimization models provide a robust theoretical basis for preferential attachment.
  • The concepts of saturation and viability are crucial for accurately describing network structure and evolution.
  • The generalized preferential attachment model offers a powerful tool for analyzing diverse complex networks.