Evolution of weighted scale-free networks in empirical data

Y.-H. Eom, C. Jeon, H. Jeong, and B. Kahng
Phys. Rev. E 77, 056105 – Published 16 May 2008

Abstract

Weighted scale-free networks exhibit two types of degree-strength relationship: linear and nonlinear relationships between them. To understand the mechanism underlying such empirical relationships, theoretical evolution models for weighted scale-free networks have been introduced for each case. However, those models have not yet been tested with empirical data. In this study, we collect temporal records of several online bulletin board systems and a movie actor network. We measure the growth rates of degree and strength of each vertex and weight of each edge within the framework of preferential attachment (PA). We also measure the probability of creating new edges between unconnected pairs of vertices. Then, based on the measured rates, linear and nonlinear growth models are constructed. We find that indeed the dynamics of creating new edges and adding weight to existing edges in a nonlocal manner is essential to reproduce the nonlinear degree-strength relationship. We also find that the degree-driven PA rule is more appropriate to real systems rather than the strength-driven one used for the linear model.

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  • Received 14 September 2007

DOI:https://doi.org/10.1103/PhysRevE.77.056105

©2008 American Physical Society

Authors & Affiliations

Y.-H. Eom, C. Jeon, and H. Jeong*

  • Department of Physics, Korea Advanced Institute of Science and Technology, 305-701 Daejon, Korea

B. Kahng

  • Department of Physics and Astronomy and Center for Theoretical Physics, Seoul National University, 151-747 Seoul, Korea

  • *hjeong@kaist.ac.kr

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Issue

Vol. 77, Iss. 5 — May 2008

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