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Preferential attachment and growth dynamics in complex systems

  • Yamasaki, Kazuko
  • Matia, Kaushik
  • Buldyrev, Sergey V.
  • Fu, Dongfeng
  • Pammolli, Fabio
  • Riccaboni, Massimo
  • Stanley, H. Eugene

Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model postulates preferential growth of the existing classes and the steady influx of new classes. According to the model, the distribution changes from a pure exponential form for zero influx of new classes to a power law with an exponential cut-off form when the influx of new classes is substantial. Predictions of the model are tested through the analysis of a unique industrial database, which covers both elementary units (products) and classes (markets, firms) in a given industry (pharmaceuticals), covering the entire size distribution. The model’s predictions are in good agreement with the data. The paper sheds light on the emergence of the exponent τ ≈ 2 observed as a universal feature of many biological, social and economic problems.

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File URL: http://mpra.ub.uni-muenchen.de/15908/1/MPRA_paper_15908.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 15908.

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Date of creation: 26 Jun 2004
Date of revision: 06 Feb 2006
Publication status: Published in Physical Review E 3.74(2006): pp. 0351031-0351034
Handle: RePEc:pra:mprapa:15908
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  1. Kaushik Matia & Dongfeng Fu & Sergey V. Buldyrev & Fabio Pammolli & Massimo Riccaboni & H. Eugene Stanley, 2005. "Statistical Properties of Business Firms Structure and Growth," Papers physics/0502081, arXiv.org.
  2. Buldyrev, S.V & Dokholyan, N.V & Erramilli, S & Hong, M & Kim, J.Y & Malescio, G & Stanley, H.E, 2003. "Hierarchy in social organization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(3), pages 653-659.
  3. De Fabritiis, Gianni & Riccaboni, Massimo & Pammolli, Fabio, 2003. "On Size and Growth of Business Firms," MPRA Paper 15866, University Library of Munich, Germany.
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