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On the formation of degree and cluster-degree correlations in scale-free networks

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  • Yao, Xin
  • Zhang, Chang-shui
  • Chen, Jin-wen
  • Li, Yan-da

Abstract

The cluster-degree of a vertex is the number of connections among the neighbors of this vertex. In this paper we study the cluster-degree of the generalized Barabási–Albert model (GBA model) whose exponent of degree distribution ranges from 2 to ∞. We present the mean-field rate equation for clustering and obtain analytically the degree-dependence of the cluster-degree. We study the distribution of the cluster-degree, which is size dependent but the tail is kept invariant for different degree exponents in the GBA model. In addition, for the degree dependence of the clustering coefficient, very different behaviors arise for different cases of the GBA model. The physical sense of the invariance property of cluster-degree is explained and more general cases are discussed. All the above theoretical results are verified by simulation.

Suggested Citation

  • Yao, Xin & Zhang, Chang-shui & Chen, Jin-wen & Li, Yan-da, 2005. "On the formation of degree and cluster-degree correlations in scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 661-673.
    • Handle: RePEc:eee:phsmap:v:353:y:2005:i:c:p:661-673
    DOI: 10.1016/j.physa.2005.01.036
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    References listed on IDEAS

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    1. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 2000. "Scale-free characteristics of random networks: the topology of the world-wide web," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 281(1), pages 69-77.
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    3. Réka Albert & Hawoong Jeong & Albert-László Barabási, 1999. "Diameter of the World-Wide Web," Nature, Nature, vol. 401(6749), pages 130-131, September.
    4. H. Jeong & B. Tombor & R. Albert & Z. N. Oltvai & A.-L. Barabási, 2000. "The large-scale organization of metabolic networks," Nature, Nature, vol. 407(6804), pages 651-654, October.
    5. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    6. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 1999. "Mean-field theory for scale-free random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(1), pages 173-187.
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    Cited by:

    1. Tam, Wai M. & Lau, Francis C.M. & Tse, Chi K. & Xia, Yongxiang & Shan, Xiuming, 2006. "Effect of clustering in a complex user network on the telephone traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 745-753.

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