Advanced Search
Article Contents
Article Contents

A sufficient condition for classified networks to possess complex network features

Abstract Related Papers Cited by
  • We investigate network features for complex networks. A sufficient condition for the limiting random variable to possess the scale free property and the high clustering property is given. The uniqueness and existence of the limit of a sequence of degree distributions for the process is proved. The limiting degree distribution and a lower bound of the limiting clustering coefficient of the graph-valued Markov process are obtained as well.
    Mathematics Subject Classification: Primary: 60D05, 90B15; Secondary: 60J20.


    \begin{equation} \\ \end{equation}
  • [1]

    R. Albert and A.-L. Barabási, Emergence of scaling in random networks, Science, 286 (1999), 509-512.doi: 10.1126/science.286.5439.509.


    R. Albert and A.-L. Barabási, Statistical mechanics of complex networks, Reviews of Mordern Physics, 74 (2002), 47-97.doi: 10.1103/RevModPhys.74.47.


    D. J. Aldous, A tractable complex network model based on the stochastic mean-field model of distance, in "Complex Networks," Lecture Notes in Physics, 650, Springer, Berlin, (2004), 51-87.


    D. J. Aldous and W. S. Kendall, Short-length routes in low-cost networks via Poisson line patterns, Advances in Applied Probability, 40 (2008), 1-21.doi: 10.1239/aap/1208358883.


    H. G. Bartel, H. J. Mucha and J. Dolata, On a modified graph-theoretic partitioning method of cluster analysis, Match-Communications in Mathematical and in Computer Chemistry, 48 (2003), 209-233.


    B. Bollobás, S. Janson and O. Riordan, The phase transition in inhomogeneous random graphs, Random Structures and Algorithms, 31 (2007), 3-122.doi: 10.1002/rsa.20168.


    A. Diaz-Guilera, Complex networks: Statics and dynamics, Advanced Summer School in Physics 2006, 885 (2007), 107-128.


    Z. P. Fan, G. R. Chen and Y. N. Zhang, A comprehensive multi-local-world model for complex networks, Physics Letters A, 373 (2009), 1601-1605.doi: 10.1016/j.physleta.2009.02.072.


    A. Ganesh and F. Xue, On the connectivity and diameter of small-world networks, Advances in Applied Probability, 39 (2007), 853-863.doi: 10.1239/aap/1198177228.


    P. Holme and B. J. Kim, Growing scale-free networks with tunable clustering, Physical Review E, 65 (2002), 026107.


    G. Lee and G. I. Kim, Degree and wealth distribution in a network, Physica A-Statistical Mechanics and its Applications, 383 (2007), 677-686.


    N. Miyoshi, T. Shigezumi, R. Uehara and O. Watanabe, Scale free interval graphs, Theoretical Computer Science, 410 (2009), 4588-4600.doi: 10.1016/j.tcs.2009.08.012.


    Y. Ou and C.-Q. Zhang, A new multimembership clustering method, Journal of Industrial and Management Optimization, 3 (2007), 619-624.doi: 10.3934/jimo.2007.3.619.


    M. M. Sørensen, b-tree facets for the simple graph partitioning polytope, Journal of Combinatorial Optimization, 8 (2004), 151-170.doi: 10.1023/B:JOCO.0000031417.96218.26.


    J. Szymański, Concentration of vertex degrees in a scale-free random graph process, Random Structures and Algorithms, 26 (2005), 224-236.doi: 10.1002/rsa.20065.


    D. J. Watts and S. H. Strogatz, Collective dynamics of 'small-world' networks, Nature, 393 (1998), 440-442.doi: 10.1038/30918.

  • 加载中

Article Metrics

HTML views() PDF downloads(67) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint