Abstract
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Pastor-Satorras, R., Vespignani, A.: Evolution and Structure of the Internet: A Statistical Physics Approach. Cambridge University Press, Cambridge (2004)
Albert, R., Jeong, H., Barabási, A.L.: The Scale-free Networks. Nature 401, 130–134 (1999)
Newman, M.E.J.: Clustering and preferential attachment in growing networks. Phys. Rev. E 64, 016131–016134 (2001)
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)
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)
Barrat, A., Barthélemy, M., Vespignani, A.: Effects of Weight on Structure and Dynamics in Complex Networks. Phys. Rev. Lett. 92, 28701–28706 (2004)
Barabási, A.-L., Albert, R.: Emergence of Scaling in Random Networks. Science 286, 509 (1999)
Albert, R., Barabási, A.-L.: Mean-field theory for scale-free random networks. Rev. Mod. Phys. 74, 47–54 (2002)
Geng, X., Li, Q.: Random Models of Scale-free Networks. Physica A: Statistical Mechanics and it’s Applications 365, 554–562 (2005)
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)
Almaas, E., Kovács, B., Viscek, T., Oltval, Z.N., Barabási, A.L.: Modeling the evolution of weighted networks. Nature 427, 839–843 (2004)
Yook, S.H., Jeong, H., Barabási, A.L., Tu, Y.: Phys. Weighted Evolving Networks. Rev. Lett. 86, 5835–5840 (2001)
Hajra, K.B., Sen, P.: Aging in citation networks. Physica A 346, 44–48 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering
About this paper
Cite this paper
Geng, X., Zhou, H., Wen, G. (2009). Evolving Model of Weighted Networks. In: Zhou, J. (eds) Complex Sciences. Complex 2009. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02469-6_37
Download citation
DOI: https://doi.org/10.1007/978-3-642-02469-6_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02468-9
Online ISBN: 978-3-642-02469-6
eBook Packages: Computer ScienceComputer Science (R0)