Advertisement

The European Physical Journal B

, Volume 38, Issue 2, pp 169–175 | Cite as

Hot spots and universality in network dynamics

  • A.-L. Barabasi
  • M. A. de MenezesEmail author
  • S. Balensiefer
  • J. Brockman
Article

Abstract.

Most complex networks serve as conduits for various dynamical processes, ranging from mass transfer by chemical reactions in the cell to packet transfer on the Internet. We collected data on the time dependent activity of five natural and technological networks, finding evidence of orders of magnitude differences in the fluxes of individual nodes. This dynamical inhomogeneity reflects the emergence of localized high flux regions or “hot spots”, carrying an overwhelming fraction of the network’s activity. We find that each system is characterized by a unique scaling law, coupling the flux fluctuations with the total flux on individual nodes, a result of the competition between the system’s internal collective dynamics and changes in the external environment. We propose a method to separate these two components, allowing us to predict the relevant scaling exponents. As high fluctuations can lead to dynamical bottlenecks and jamming, these findings have a strong impact on the predictability and failure prevention of complex transportation networks.

Keywords

Transportation Network Individual Node Collective Dynamic Failure Prevention Flux Region 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    The Cooperative Association for Internet Data Analysis (http://www.caida.org), BioCyc Knowledge Database (http://biocyc.org), Yeast Protein Complex Database (http://yeast.cellzome.com) and othersGoogle Scholar
  2. 2.
    Handbook of Graphs and Networks, edited by S. Bornholdt, H.G. Schuster (Wiley-VCH, Berlin, 2002)Google Scholar
  3. 3.
    S.N. Dorogovtsev, J.F.F. Mendes, Adv. Phys. 51, 1079 (2002)ADSCrossRefGoogle Scholar
  4. 4.
    R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002)ADSCrossRefGoogle Scholar
  5. 5.
    S.H. Strogatz, Nature 410, 268 (2001)ADSCrossRefGoogle Scholar
  6. 6.
    W.E. Leland, M.S. Taqqu, W. Willinger, D.V. Wilson, IEEE/ACM Trans. Networking 2, 1 (1994)CrossRefGoogle Scholar
  7. 7.
    M. Crovella, A. Bestavros, IEEE/ACM Trans. Networking 5, 835 (1997)CrossRefGoogle Scholar
  8. 8.
    I. Csabai, J. Phys. A 27, L417 (1994)Google Scholar
  9. 9.
    K. Fukuda, M. Takayasu, H. Takayasu, Physica A 287, 289 (2000)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    A.L. Goldberger, L.A.N. Amaral, J.M. Hausdorff, P.C. Ivanov, C.K. Peng, H.E. Stanley, Proc. Natl. Acad. Sci. USA 99, 2466 (2002)ADSCrossRefGoogle Scholar
  11. 11.
    R.N. Mantegna, H.E. Stanley, Nature 376, 46 (1995)ADSCrossRefGoogle Scholar
  12. 12.
    K.-I. Goh, B. Kahng, D. Kim, Phys. Rev. Lett. 87, 278701 (2001)ADSCrossRefGoogle Scholar
  13. 13.
    K.-I. Goh, E.S. Oh, H. Jeong, B. Kahng, D. Kim, Proc. Natl. Acad. Sci. USA 99, 12583 (2002)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    S. Uhlig, O. Bonaventure, Technical Report Infonet-TR-10, University of Namur, June 2001 http://www.infonet.fundp.ac.be/doc/tr/ Infonet-TR-2001-10.htmlGoogle Scholar
  15. 15.
    D. Garlaschelli, S. Battiston, M. Castri, Vito D.P. Servedio, G. Caldarelli, cond-mat/0310503Google Scholar
  16. 16.
    E. Almaas, B. Kovacs, T. Vicsek, Z.N. Oltvai, A.-L. Barabási, Nature (in press)Google Scholar
  17. 17.
    S. Redner, A Guide to First-Passage Processes (Cambridge University Press, USA, 2001)Google Scholar
  18. 18.
    S. Havlin, D. Ben-Avraham, Adv. Phys. 36, 695 (1987)ADSCrossRefGoogle Scholar
  19. 19.
    M. Argollo de Menezes, A.-L. Barabási, to appear in Phys. Rev. Lett. cond-mat/0306304Google Scholar
  20. 20.
    S. Lawrence, L. Giles, Nature 400, 107 (1999)ADSCrossRefGoogle Scholar
  21. 21.
    R. Albert, H. Jeong, A.-L. Barabási, Nature 401, 130 (1999)ADSCrossRefGoogle Scholar
  22. 22.
    B. Kahng, Y. Park, H. Jeong, Phys. Rev. E 66, 046107 (2002)ADSCrossRefGoogle Scholar
  23. 23.
    B. Tadic, Physica A 293, 273 (2001)ADSCrossRefGoogle Scholar
  24. 24.
    A. Vazquez, R. Pastor-Satorras, A. Vespignani, Phys. Rev. E 65, 066130 (2002)ADSCrossRefGoogle Scholar
  25. 25.
    S.-H. Yook, H. Jeong, A.-L. Barabási, Proc. Nat. Acad. Sci. 99, 13382 (2002)ADSCrossRefGoogle Scholar
  26. 26.
    M. Barthélémy, B. Gondran, E. Guichard, Phys. Rev. E 66, 056110 (2002)ADSCrossRefGoogle Scholar
  27. 27.
    K.A. Eriksen, I. Simonsen, S. Maslov, K. Sneppen, Phys. Rev. Lett. 90, 148701 (2003)ADSCrossRefGoogle Scholar
  28. 28.
    R. Ferrer, C. Janssen, R.V. Solé, Phys. Rev. E 63, 32767 (2001)Google Scholar
  29. 29.
    A.-L. Barabási, R. Albert, Science 286, 509 (1999)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    P. Erdös, A. Rényi, Publ. Math. Inst. Hung. Acad. Sci. 5, 17 (1960)Google Scholar
  31. 31.
    A.-L. Barabási, H.E. Stanley Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, 1995)Google Scholar
  32. 32.
    Dynamics of Fractal Surfaces, edited F. Family, T. Vicsek (World Scientific, Singapore, 1991)Google Scholar
  33. 33.
    M. Argollo de Menezes, A. Vazquez, A.-L. Barabási, preparationGoogle Scholar
  34. 34.
    J.D. Noh, H. Rieger, cond-mat/0307719 (2003)Google Scholar
  35. 35.
    Y. Moreno, R. Pastor-Satorras, A. Vázquez, A. Vespignani, cond-mat/0209474Google Scholar
  36. 36.
    J. Hasty, J.J. Collins, Nat. Genet. 31, 13 (2002)CrossRefGoogle Scholar
  37. 37.
    N.S. Holter, A. Maritan, M. Cieplak, N. Fedoroff, J.R. Banavar, Proc. Natl. Acad. Sci. USA 98, 1693 (2001)ADSCrossRefGoogle Scholar
  38. 38.
    H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai, A.-L. Barabási, Nature 407, 651 (2000)ADSCrossRefGoogle Scholar
  39. 39.
    H. Jeong, S. Mason, A.-L. Barabási, Z.N. Oltvai, Nature 411, 41 (2001)ADSCrossRefGoogle Scholar
  40. 40.
    E. Ravasz, A.L. Somera, D.A. Mongru, Z.N. Oltvai, A.-L. Barabási, Science 297, 1551 (2002)ADSCrossRefGoogle Scholar
  41. 41.
    R.N. Mantegna, H.E. Stanley, An Introduction to Econophysics: Correlations and Complexity in Finance (Cambridge Univ. Press, New York, 2000)Google Scholar
  42. 42.
    J.P. Bouchaud, M. Potters, Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management, 2nd edn. (Cambridge University Press, USA, 2000)Google Scholar
  43. 43.
    L. Gillemot, J. Toyli, J. Kertesz, K. Kaski, Physica A 282, 304 (2000)ADSCrossRefGoogle Scholar
  44. 44.
    J. Hasty, J. Pradines, M. Dolnik, J.J. Collins, Proc. Natl. Acad. Sci. USA 97, 2075 (2000)ADSCrossRefGoogle Scholar
  45. 45.
    M.B Elowitz, A.J. Levine, E.D. Siggia, P.S. Swain, Science 297, 1183 (2002)ADSCrossRefGoogle Scholar
  46. 46.
    M. Barthélémy, S.V. Buldyrev, S. Havlin, H.E. Stanley, Phys. Rev. E 61, R3283 (2000)Google Scholar
  47. 47.
    L. de Arcangelis, S. Redner, A. Coniglio, Phys. Rev. B 34, 4656 (1986)ADSCrossRefGoogle Scholar
  48. 48.
    J. Helsing, J. Axell, G. Grimvall, Phys. Rev. B 39, 9231 (1989)ADSCrossRefGoogle Scholar
  49. 49.
    Fractals in Science, etited by A. Bunde, S. Havlin (Springer, Berlin, 1994)Google Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  • A.-L. Barabasi
    • 1
  • M. A. de Menezes
    • 1
    Email author
  • S. Balensiefer
    • 2
  • J. Brockman
    • 2
  1. 1.Department of PhysicsUniversity of Notre DameNotre DameUSA
  2. 2.Department of Computer Science and EngineeringUniversity of Notre DameNotre DameUSA

Personalised recommendations