Some New Applications of Network Growth Models

  • Gourab Ghoshal
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)

The study and analysis of complex networks has in recent times sparked widespread attention from the scientific community [1, 2, 3]. This interest has been spurred partly by researchers recognizing networks as useful representations of real-world complex systems, and also due to the widespread availability of computing resources, enabling them to gather and analyze data on a scale much larger than before. Studies have ranged from large-scale empirical analysis of the World Wide Web, social networks and biological systems, to the development of theoretical models and tools to explore the various properties of these systems [4, 5].

A topic that has garnered significant interest is the subject of growing networks, inspired by real-world examples such as that of the Internet, the World Wide Web and scientific citation networks [6, 7, 8]. The particular case of the World Wide Web has led to what is perhaps the best-known body of work on this topic: the preferential attachment model [9, 10], in which vertices are added to a network with edges that attach to pre-existing vertices with probabilities depending on those vertices’ degrees. When the attachment probability is precisely linear in the degree of the target vertex, the resulting degree sequence has a power-law tail, in the limit of large network size. The appearance of the power-law tail is what first led to the popularity of growth models as a method to describe network evolution, as most real-world networks appear to have degree distributions that are approximately power laws.


Degree Distribution Search Time Virtual Network Degree Correlation Giant Component 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The author thanks Mark Newman and Brian Karrer for illuminating discussions. This work was funded by the James S. McDonnell Foundation.


  1. 1.
    R. Albert and A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002).CrossRefMATHGoogle Scholar
  2. 2.
    S. N. Dorogovtsev and J. F. F. Mendes, Adv. Phys. 51, 1079 (2002).CrossRefGoogle Scholar
  3. 3.
    M. E. J. Newman, SIAM Review 45, 167 (2003).CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    D. J. Watts and S. H. Strogatz, Nature 393, 440 (1998).CrossRefGoogle Scholar
  5. 5.
    R. J. Williams and N. D. Martinez, Nature 404, 180 (2000).CrossRefGoogle Scholar
  6. 6.
    R. Albert, H. Jeong and A.-L. Barabási, Nature 401, 130 (1999).CrossRefGoogle Scholar
  7. 7.
    D. J. de S. Price, Science 149, 510 (1965).CrossRefGoogle Scholar
  8. 8.
    S. Redner, Eur. Phys. J. B 4, 131 (1998).CrossRefGoogle Scholar
  9. 9.
    D. J. de S. Price, J. Amer. Soc. Inform. Sci. 27, 292 (1976).CrossRefGoogle Scholar
  10. 10.
    A.-L. Barabási and R. Albert, Science 286, 509 (1999).CrossRefMathSciNetGoogle Scholar
  11. 11.
    E. Ben-Naim and P. L. Krapivsky, J. Phys. A: Math. Theor. 40, 8607 (2007).CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    C. Moore, G. Ghoshal and M. E. J. Newman, Phys. Rev. E 74, 036121 (2006).CrossRefMathSciNetGoogle Scholar
  13. 13.
    J. Saldaña, Phys. Rev. E 75, 027102 (2007).CrossRefMathSciNetGoogle Scholar
  14. 14.
    T. Hong, in Peer-to-Peer, Harnessing the Benefits of a Disruptive Technology, edited by Andy Oram (O'Reilly, Sebastopol, CA, 2001), Chap. 14, pp. 203–241.Google Scholar
  15. 15.
    L. A. Adamic, R. M. Lukose, A. R. Puniyani and B. A. Huberman, Phys. Rev. E 64, 046135 (2001).CrossRefGoogle Scholar
  16. 16.
    N. Sarshar, P. O. Boykin and V. P. Roychowdhury, Fourth International Conference on Peer-to-Peer Computing, pp. 2–9, Washington, D.C. (2004).Google Scholar
  17. 17.
    G. Paul, T. Tanizawa, S. Havlin and H. E. Stanley, Eur. Phys. J. B 38, 187 (2004).CrossRefGoogle Scholar
  18. 18.
    R. Cohen, K. Erez, D. ben-Avraham and S. Havlin, Phys. Rev. Letts. 85, 4626 (2000).CrossRefGoogle Scholar
  19. 19.
    D. S. Callaway, M. E. J. Newman, S. H. Strogatz and D. J. Watts, Phys. Rev. Letts. 85, 5468 (2000).CrossRefGoogle Scholar
  20. 20.
    M. E. J. Newman and G. Ghoshal, Phys. Rev. Letts. 100, 138701 (2008).CrossRefGoogle Scholar
  21. 21.
    B. Rezai, N. Sarshar, V. Roychowdhury and P. Oscar Boykin, Physica A 381, 497 (2007).CrossRefGoogle Scholar
  22. 22.
    A. E. Motter, Phys. Rev. Letts. 93, 098701 (2004).CrossRefGoogle Scholar
  23. 23.
    P. L. Krapivsky and S. Render, Phys. Rev. E 63, 066123 (2001).CrossRefGoogle Scholar
  24. 24.
    G. Ghoshal and M. E. J. Newman, Eur. Phys. J. B, 58, 175 (2007).CrossRefGoogle Scholar
  25. 25.
    M. Molloy and B. Reed, Random Struct. Algorithms 6, 161 (1995).CrossRefMATHMathSciNetGoogle Scholar
  26. 26.
    B. Karrer and G. Ghoshal, Eur. Phys. J B, 62, 239 (2008).CrossRefGoogle Scholar
  27. 27.
    J. S. Kong and V. P. Roychowdhury, e-print arXiv:0711.3263v2.Google Scholar

Copyright information

© Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Physics and Michigan Center for Theoretical PhysicsUniversity of MichiganMIUSA

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