Preferential Attachment and Growth Dynamics in Complex Systems

Physical Review E, 2006

4 Pages Posted: 21 Nov 2007 Last revised: 24 Dec 2007

See all articles by Kazuko Yamasaki

Kazuko Yamasaki

Tokyo University of Information Sciences

Kaushik Matia

Boston University - Department of Physics

Fabio Pammolli

Polytechnic University of Milan - Department of Management, Economics and Industrial Engineering; CERM Foundation

Sergey Buldyrev

Yeshiva University - Department of Physics

Massimo Riccaboni

KU Leuven - Department of Managerial Economics, Strategy, and Innovation; IMT Institute for Advanced Studies

H. Eugene Stanley

Boston University - Center for Polymer Studies

Dongfeng Fu

Boston University - Department of Physics

Abstract

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 tau approximately 2 observed as a universal feature of many biological, social and economic problems.

Suggested Citation

Yamasaki, Kazuko and Matia, Kaushik and Pammolli, Fabio and Buldyrev, Sergey and Riccaboni, Massimo and Stanley, H. Eugene and Fu, Dongfeng, Preferential Attachment and Growth Dynamics in Complex Systems. Available at SSRN: https://ssrn.com/abstract=1031658

Kazuko Yamasaki (Contact Author)

Tokyo University of Information Sciences ( email )

Tokyo
Japan

Kaushik Matia

Boston University - Department of Physics ( email )

590 Commonwealth Avenue
Boston, MA 02215
United States

Fabio Pammolli

Polytechnic University of Milan - Department of Management, Economics and Industrial Engineering ( email )

Via Lambruschini 4C - building 26/A
Milano, 20156
Italy

CERM Foundation ( email )

Via Fiorentina, 1
Siena, Siena 53100
Italy

HOME PAGE: http://www.cermlab.it

Sergey Buldyrev

Yeshiva University - Department of Physics ( email )

500 West, 185th Street
New York, NY 10033
United States

Massimo Riccaboni

KU Leuven - Department of Managerial Economics, Strategy, and Innovation ( email )

Naamsestraat 69 bus 3500
Leuven, 3000
Belgium

IMT Institute for Advanced Studies ( email )

Complesso San Micheletto
Lucca, 55100
Italy

H. Eugene Stanley

Boston University - Center for Polymer Studies ( email )

Boston, MA 02215
United States

Dongfeng Fu

Boston University - Department of Physics ( email )

590 Commonwealth Avenue
Boston, MA 02215
United States

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