Evolving Model of Weighted Networks

  • Xianmin Geng
  • Hongwei Zhou
  • Guanghui Wen
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 5)


In this paper, in order to search the reason of the phenomena of power- law in the weighted networks, we present a general model for the growth of weighted networks that couples of new edges and vertices and the weights’ and intrinsic strengths’ dynamical evolution. This model is based on a simple weight and intrinsic strength driven dynamics and generates networks exhibiting the statistical properties observed in several real-world systems. Within this model we not only yields the scale-free behavior for the weight, strength and degree distributions, but also we give the analytical computation of the distributions of the weight, the strength and the degree .Simultaneity, by way of contrasting our results with those of the random model, we found the preferential attachment is necessary to the phenomena of scale-free of the strength and degree distributions. Finally, we found the analytical results are good consistent with those of numerical simulation. The conclusion from this model is helpful to the investigation of the topological role of weight and strength.


weighted network scale-free network degree distribution intrinsic strength 


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  1. 1.
    Pastor-Satorras, R., Vespignani, A.: Evolution and Structure of the Internet: A Statistical Physics Approach. Cambridge University Press, Cambridge (2004)CrossRefzbMATHGoogle Scholar
  2. 2.
    Albert, R., Jeong, H., Barabási, A.L.: The Scale-free Networks. Nature 401, 130–134 (1999)CrossRefGoogle Scholar
  3. 3.
    Newman, M.E.J.: Clustering and preferential attachment in growing networks. Phys. Rev. E 64, 016131–016134 (2001)CrossRefGoogle Scholar
  4. 4.
    Barabási, A.-L., Jeong, H., Néda, Z., Ravasz, E., Schubert, A., Vicsek, T.: Evolution of the social network of scientific collaborations. Physica A 50, 590–596 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Barrat, A., Barthélemy, M., Pastor-Satorras, R., Vespignani, A.: The architecture of complex weighted networks. Proc. Natl. Sci. U.S.A. 101, 3747–3752 (2004)CrossRefGoogle Scholar
  6. 6.
    Barrat, A., Barthélemy, M., Vespignani, A.: Effects of Weight on Structure and Dynamics in Complex Networks. Phys. Rev. Lett. 92, 28701–28706 (2004)CrossRefGoogle Scholar
  7. 7.
    Barabási, A.-L., Albert, R.: Emergence of Scaling in Random Networks. Science 286, 509 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Albert, R., Barabási, A.-L.: Mean-field theory for scale-free random networks. Rev. Mod. Phys. 74, 47–54 (2002)CrossRefzbMATHGoogle Scholar
  9. 9.
    Geng, X., Li, Q.: Random Models of Scale-free Networks. Physica A: Statistical Mechanics and it’s Applications 365, 554–562 (2005)CrossRefGoogle Scholar
  10. 10.
    Krause, A.E., Frank, K.A., Mason, D.M., Ulanowicz, R.E., Taylor, W.W.: Weighted Evolving Networks: Coupling Topology and Weight Dynamics. Nature 426, 282–286 (2003)CrossRefGoogle Scholar
  11. 11.
    Almaas, E., Kovács, B., Viscek, T., Oltval, Z.N., Barabási, A.L.: Modeling the evolution of weighted networks. Nature 427, 839–843 (2004)CrossRefGoogle Scholar
  12. 12.
    Yook, S.H., Jeong, H., Barabási, A.L., Tu, Y.: Phys. Weighted Evolving Networks. Rev. Lett. 86, 5835–5840 (2001)CrossRefGoogle Scholar
  13. 13.
    Hajra, K.B., Sen, P.: Aging in citation networks. Physica A 346, 44–48 (2005)CrossRefGoogle Scholar

Copyright information

© ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering 2009

Authors and Affiliations

  • Xianmin Geng
    • 1
  • Hongwei Zhou
    • 1
    • 2
  • Guanghui Wen
    • 3
  1. 1.College of scienceNanjing University of Aeronautics and AstronauticsNanjingP.R. China
  2. 2.Department of MathematicsNanjing Xiao Zhuang CollegeNanjingP.R. China
  3. 3.College of EngineeringPeking UniversityBeijingP.R. China

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