Fingerprint for Network Topologies

  • Yuchun Guo
  • Changjia Chen
  • Shi Zhou
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 5)


A network’s topology information can be given as an adjacency matrix. The bitmap of sorted adjacency matrix (BOSAM) is a network visualisation tool which can emphasise different network structures by just looking at reordered adjacent matrixes. A BOSAM picture resembles the shape of a flower and is characterised by a series of ‘leaves’. Here we show and mathematically prove that for most networks, there is a self-similar relation between the envelope of the BOSAM leaves. This self-similar property allows us to use a single envelope to predict all other envelopes and therefore reconstruct the outline of a network’s BOSAM picture. We analogise the BOSAM envelope to human’s fingerprint as they share a number of common features, e.g. both are simple, easy to obtain, and strongly characteristic encoding essential information for identification.


complex network mixing patterns visualisation BOSAM 


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  1. 1.
    Wasserman, S., Faust, K.: Social Network Analysis. Cambridge University Press, Cambridge (1994)CrossRefzbMATHGoogle Scholar
  2. 2.
    Watts, J.: Small Worlds: The Dynamics of Networks between Order and Randomness. Princeton Univeristy Press, New Jersey (1999)zbMATHGoogle Scholar
  3. 3.
    Barabási, A., Albert, R.: Science 286, 509 (1999)Google Scholar
  4. 4.
    Strogatz, S.H.: Nature 410, 268 (2001)Google Scholar
  5. 5.
    Albert, R., Barabasi, A.L.: Rev. Mod. Phys. 74, 47 (2002)Google Scholar
  6. 6.
    Maslov, S., Sneppen, K.: Science 296, 910 (2002)Google Scholar
  7. 7.
    Bornholdt, S., Schuster, H.G.: Handbook of Graphs and Networks - From the Genome to the Internet. Wiley-VCH, Weinheim (2002)CrossRefzbMATHGoogle Scholar
  8. 8.
    Newman, M.: SIAM Review 45, 167 (2003a)Google Scholar
  9. 9.
    Dorogovtsev, S.N., Mendes, J.F.F.: Evolution of Networks - From Biological Nets to the Internet and WWW. Oxford University Press, Oxford (2003)CrossRefzbMATHGoogle Scholar
  10. 10.
    Pastor-Satorras, R., Vespignani, A.: Evolution and Structure of the Internet - A Statistical Physics Approach. Cambridge University Press, Cambridge (2004)CrossRefzbMATHGoogle Scholar
  11. 11.
    Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.-U.: Physics Reports 424, 175 (2006)Google Scholar
  12. 12.
    Newman, M., Barabasi, A.-L., Watts, D. (eds.): The Structure and Dynamics of Networks. Princeton University Press, Princeton (2006)Google Scholar
  13. 13.
    Alvarez-Hamelin, J.-I., Dall’Asta, L., Barrat, A., Vespignani, A.: Scholar
  14. 14.
    Guo, Y., Chen, C., Zhou, S.: Electronics Letters 43, 597 (2007)Google Scholar
  15. 15.
    Chakrabarti, D., Faloutsos, C., Zhan, Y.P.: International Journal of Human Computer Studies 65, 434 (2007)Google Scholar
  16. 16.
    Vazquez, A., Boguñá, M., Moreno, Y., Pastor-Satorras, R., Vespignani, A.: Phys. Rev. E 67 (2003)Google Scholar
  17. 17.
    Mahadevan, P., Krioukov, D., Fall, K., Vahdat, A.: Proc. of SIGCOMM 2006, pp. 135–146. ACM Press, New York (2006a)Google Scholar
  18. 18.
    Newman, M.E.J.: Phys. Rev. E 67 (2003b)Google Scholar
  19. 19.
    Newman, M.E.J.: Phys. Rev. Lett. 89 (2002)Google Scholar
  20. 20.
    Zhou, S., Mondragon, R.J.: IEEE Comm. Lett. 8, 180 (2004a)Google Scholar
  21. 21.
    Zhou, S., Mondragon, R.: New Journal of Physics 9, 1 (2007)Google Scholar
  22. 22.
    Mahadevan, P., Krioukov, D., Fomenkov, M., Huffaker, B., Dimitropoulos, X., Clffay, K., Vahdat, A.: Comput. Commun. Rev. 36, 17 (2006b)Google Scholar
  23. 23.
    Hogg, R.V., Craig, A.T.: Introduction to Mathematical Statistics, 3rd edn. Macmillan, Basingstoke (1970)zbMATHGoogle Scholar
  24. 24.
    Rose, C., Smith, M.D.: Order Statistics. Springer, New York (2002)zbMATHGoogle Scholar
  25. 25.
    Erdös, P., Rényi, A.: Publ. Math. Debrecen 6, 290 (1959)Google Scholar
  26. 26.
    Zhou, S., Mondragón, R.J.: Phys. Rev. E 70 (2004b)Google Scholar
  27. 27.
    Zhou, S.: Phys. Rev. E 74 (2006)Google Scholar
  28. 28.
    Zhou, S., Zhang, G.-Q., Zhang, G.-Q.: IET Commun. 1, 209 (2007)Google Scholar
  29. 29.
    Newman, M.: Phys. Rev. E 64, 016131 (2001a)Google Scholar
  30. 30.
    Newman, M.: Phys. Rev. E 64 (2001b)Google Scholar
  31. 31.
    Colizza, V., Flammini, A., Maritan, A., Vespignani, A.: Physica A 352, 1 (2005)Google Scholar
  32. 32.
    Internet Topology Data Kit (ITDK) #0403,
  33. 33.
    The Cooperative Association For Internet Data Analysis (CAIDA),
  34. 34.
    Guimerá, R., Danon, L., Daz-Guilera, A., Giralt, F., Arenas, A.: Phys. Rev. E 68, 065103(R) (2003)Google Scholar

Copyright information

© ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering 2009

Authors and Affiliations

  • Yuchun Guo
    • 1
  • Changjia Chen
    • 1
  • Shi Zhou
    • 2
  1. 1.Beijing Jiaotong UniversityChina
  2. 2.University College LondonUnited Kingdom

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