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The European Physical Journal B

, Volume 38, Issue 2, pp 223–230 | Cite as

Number of cycles in off-equilibrium scale-free networks and in the Internet at the Autonomous System Level

  • G. BianconiEmail author
Article

Abstract.

In order to characterize networks in the scale-free network class we study the frequency of cycles of length h that indicate the ordering of network structure and the multiplicity of paths connecting two nodes. In particular we focus on the scaling of the number of cycles with the system size in off-equilibrium scale-free networks. We observe that each off-equilibrium network model is characterized by a particular scaling in general not equal to the scaling found in equilibrium scale-free networks. We claim that this anomalous scaling can occur in real systems and we report the case of the Internet at the Autonomous System Level.

Keywords

Network Model Network Structure System Level Real System System Size 
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.

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References

  1. 1.
    R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002)ADSCrossRefGoogle Scholar
  2. 2.
    S. Strogatz, Nature 410, 268 (2001)ADSCrossRefGoogle Scholar
  3. 3.
    S.N. Dorogovtsev, J.F.F. Mendes, Evolution of Networks (Oxford University Press, Oxford, 2003)Google Scholar
  4. 4.
    R. Albert, H. Jeong, A.-L. Barabási, Nature 406, 378 (2000)ADSCrossRefGoogle Scholar
  5. 5.
    R. Pastor-Satorras, A. Vázquez, A. Vespignani, Phys. Rev. Lett. 87, 2587011 (2001)CrossRefGoogle Scholar
  6. 6.
    A. Vásquez, R. Pastor-Satorras, A. Vespignani, Phys. Rev. E 65, 066130 (2002)ADSCrossRefGoogle Scholar
  7. 7.
    S. Maslov, K. Sneppen, Science 296, 910 (2002)ADSCrossRefGoogle Scholar
  8. 8.
    S. Maslov, K. Sneppen, A. Zaliznyak, cond-mat/0205379 (2002)Google Scholar
  9. 9.
    D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998)ADSCrossRefGoogle Scholar
  10. 10.
    G. Caldarelli, R. Pastor-Satorras, A. Vespignani, cond-mat/0212026 (2002)Google Scholar
  11. 11.
    E. Ravasz, A.L. Somera, D.A. Mongru, Z.N. Oltvai, A.-L. Barabási, Science 297, 1551 (2002)ADSCrossRefGoogle Scholar
  12. 12.
    R. Milo, S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, U. Alon, Science 298, 824 (2002)ADSCrossRefGoogle Scholar
  13. 13.
    G. Bianconi, A. Capocci, Phys. Rev. Lett. 90, 078701 (2003)ADSCrossRefGoogle Scholar
  14. 14.
    S. Itzkovitz, R. Milo, N. Kashtan, G. Ziv, U. Alon, Phys. Rev. E 68, 026127 (2003)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    A.-L. Barabási, R. Albert, Science 286, 509 (1999)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    A.-L. Barabási, R. Albert, H. Jeong, Physica A 272, 173 (1999)ADSCrossRefGoogle Scholar
  17. 17.
    M. Faloutsos, P. Faloustsos, C. Faloutsos, ACM SIGCOMM ‘99 Comput. Commun. Rev. 29, 251 (1999)CrossRefGoogle Scholar
  18. 18.
    G. Caldarelli, R. Marchetti, L. Pietronero, Europhys. Lett. 52, 386 (2000)ADSCrossRefGoogle Scholar
  19. 19.
    S.-H. Yook, H. Jeong, A.-L. Barabási, P. Natl. Acad. Sci. USA 99, 13382 (2002)ADSCrossRefGoogle Scholar
  20. 20.
    B. Bollobás, Random Graphs (Accademic Press, London, 1985)Google Scholar
  21. 21.
    P. Erdös, A. Rényi, Publ. Math. Inst. Hung. Acad. Sci. 5, 17 (1960)Google Scholar
  22. 22.
    P.M. Gleiss, P.F. Stadler, A. Wagner, D.A. Fell, Adv. Complex Syst. 4, 207 (2001)MathSciNetCrossRefGoogle Scholar
  23. 23.
    K. Klemm, V. Egu\’iluz, Phys. Rev. E 65, 057102 (2002)ADSCrossRefGoogle Scholar
  24. 24.
    B. Bollobás, O.R. Riordan, in Handbook of Graphs and Networks edited by S. Bornholdt, H.G. Schuster (Wiley-VCH, Berlin, 2002), pp. 1-34Google Scholar
  25. 25.
    G. Szabó, M. Alava, J. Kertész, Phys. Rev. E 67, 056102 (2003)ADSCrossRefGoogle Scholar
  26. 26.
    G. Bianconi, A.-L. Barabási, Phys. Rev. Lett. 86, 5632 (2001)ADSCrossRefGoogle Scholar
  27. 27.
    G. Bianconi, A.-L. Barabási, Europhys. Lett. 54, 436 (2001)ADSCrossRefGoogle Scholar
  28. 28.
    S.N. Dorogovtsev, J.F.F. Mendes, Phys. Rev. E 62, 1842 (2000)ADSCrossRefGoogle Scholar
  29. 29.
    S.N. Dorogovtsev, J.F.F. Mendes, Phys. Rev. E 63, 056125 (2001)ADSCrossRefGoogle Scholar
  30. 30.
    K. Klemm, V.M. Eguiluz, Phys. Rev. E 65, 036123 (2002)ADSCrossRefGoogle Scholar
  31. 31.
    S. Wuchty, Z.N. Oltvai, A.-L. Barabási, Nature Genetics 35, 176 (2003)CrossRefGoogle Scholar
  32. 32.
    G. Bianconi, G. Caldarelli, A. Capocci, cond-mat/0310339 (2003)Google Scholar
  33. 33.
    G. Caldarelli, P. De Los Rios, L. Pietronero, cond-mat/0307610 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  1. 1.The Abdus Salam International Center for Theoretical PhysicsTriesteItaly

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