Skip to main content
SpringerLink
Log in

Random continuous model of scale-free networks

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

There are a lot of continuous evolving networks in real world, such as Internet, www network, etc. The evolving operation of these networks are not an equating interval of time by chance. In this paper, the author proposes a new mathematical model for the mechanism of continuous single preferential attachment on the scale free networks, and counts the distribution of degree using stochastic analysis. Namely, the author has established the random continuous model of the network evolution of which counting process determines the operating number, and has proved that this system self-organizes into scale-free structures with scaling exponent γ = 3+ α/m.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. L. Barabási and R. Albert, Emergence of scaling in random networks, Science, 1999, 28: 509–512.

    Google Scholar 

  2. S. H. Strogatz, Exploring complex networks, Nature, 2001, 410: 268–276.

    Article  Google Scholar 

  3. B. A. Huberman and L. A. Adamic, Growth dynamics of the World-Wide Web, Nature, 1999, 401: 131.

    Google Scholar 

  4. R. Albert and A. L. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys., 1999, 74: 47–97.

    Article  Google Scholar 

  5. R. Albert and A. L. Barabási, Topology of evolving networks: Local events and universality, Phys. Rev. Lett., 2000, 85: 5234–5237.

    Article  Google Scholar 

  6. M. E. J. Newman, The structure and function of complex networks, http://www.arxiv.org/condmat/0303516v1, 25 Mar. 2003.

  7. R. Albert and A. L. Brarbási, Statistical mechanics of complex networks, Rev. of Modern Phy., 2002, 74(1): 47–97.

    Article  MATH  Google Scholar 

  8. B. Bollobas, O. Riordan, J. Spencer, et al., The degree sequence of a scale-free random graph process, Random Structures and Algorithms, 2001, 18(3): 279–290.

    Article  MATH  MathSciNet  Google Scholar 

  9. P. Erdös and A. Rényi, On the evolution of random graphs, Magyar Tud. Akad. Mat. Kutató Int. Közl, 1960(5): 17–61.

  10. D. J. Watts and S. H. Strogatz, Collective dynamics of small-world networks, Nature, 1998, 393: 440.

    Article  Google Scholar 

  11. S. Milgram, The small world problem, Psychology Today, 1967, 2(1): 61–67.

    Google Scholar 

  12. Z. M. Ma, The 3rd China Meeting on Complex Networks, Beijing, 2005.

  13. G. L. Gong, Introductions of Stochastic Differential Equations, Press of Peking University, Beijing, 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Xianmin Geng

Authors
  1. Xianmin Geng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xianmin Geng.

Additional information

This research is supported by the National Natural Science Foundation of China under Grant No. 10671197.

This paper was recommended for publication by Editor Jinhu LÜ.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Geng, X. Random continuous model of scale-free networks. J Syst Sci Complex 24, 218–224 (2011). https://doi.org/10.1007/s11424-011-8076-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-011-8076-6

Key words

Search

Navigation