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Preferential attachment and growth dynamics in complex systems.

Kazuko Yamasaki1, Kaushik Matia, Sergey V Buldyrev

  • 1Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 10, 2006
PubMed
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We developed a generalized preferential attachment model to explain class size distribution in complex systems. The model accurately predicts power-law distributions observed in real-world data, like the pharmaceutical industry.

Area of Science:

  • Complex Systems Science
  • Network Theory
  • Industrial Organization

Background:

  • Complex systems exhibit emergent properties, including characteristic distributions of element classes.
  • Understanding the dynamics of class size distribution is crucial for analyzing system evolution.

Purpose of the Study:

  • To propose a generalized preferential attachment model for describing class size distributions.
  • To investigate the transition from exponential to power-law distributions with new class influx.
  • To validate the model using a comprehensive pharmaceutical industry dataset.

Main Methods:

  • Developed a generalized preferential attachment model incorporating preferential growth and new class influx.
  • Analyzed a unique industrial database covering products, markets, and firms in the pharmaceutical sector.

Related Experiment Videos

  • Compared model predictions against empirical data across the full size distribution.

    • Main Results:

    • The model accurately predicts class size distributions, transitioning from exponential to power-law with exponential cut-off as new classes increase.
    • Empirical data from the pharmaceutical industry strongly supports the model's predictions.
    • The study illuminates the origin of the exponent tau ≈ 2 in various complex systems.

    Conclusions:

    • The generalized preferential attachment model provides a robust framework for understanding class size distributions in complex systems.
    • The model's success in the pharmaceutical industry suggests its applicability to diverse biological, social, and economic phenomena.
    • This work offers insights into the universality of power-law exponents in complex systems.