Bipartite Graphs as Models of Complex Networks

  • Jean-Loup Guillaume
  • Matthieu Latapy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3405)

Abstract

We propose here the first model which achieves the following challenges: it produces graphs which have the three main wanted properties (clustering, degree distribution, average distance), it is based on some real-world observations, and it is sufficiently simple to make it possible to prove its main properties. This model consists in sampling a random bipartite graph with prescribed degree distribution. Indeed, we show that any can be viewed as a bipartite graph with some specific characteristics, and that its main properties can be viewed as consequences of this underlying structure.

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References

  1. 1.
    Abello, J., Pardalos, P.M., Resende, M.G.C.: On maximum clique problems in very large graphs. In: External Memory Algorithms. AMS-DIMACS Series on Discrete Mathematics and Theoretical Computer Science, vol. 50 (1999)Google Scholar
  2. 2.
    Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Reviews of Modern Physics 74, 47 (2002)CrossRefMathSciNetMATHGoogle Scholar
  3. 3.
    Albert, R., Jeong, H., Barabási, A.-L.: Diameter of the world wide web. Nature 401, 130–131 (1999)CrossRefGoogle Scholar
  4. 4.
    Source code for the random bipartite graph generator, http://www.liafa.jussieu.fr/~guillaume/programs/
  5. 5.
    Dorogovtsev, S.N., Mendes, J.F.F.: Evolution of networks. Adv. Phys. 51, 1079–1187 (2002)CrossRefGoogle Scholar
  6. 6.
    Ferrer, R., Solé, R.V.: The small-world of human language. Proceedings of the Royal Society of London B268, 2261–2265 (2001)Google Scholar
  7. 7.
    Garey, M., Johnson, D.: Computers and Intractability; A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, New York (1979)MATHGoogle Scholar
  8. 8.
    Govindan, R., Tangmunarunkit, H.: Heuristics for internet map discovery. In: IEEE INFOCOM 2000, Tel Aviv, Israel, March 2000, pp. 1371–1380. IEEE, Los Alamitos (2000)Google Scholar
  9. 9.
    Jeong, H., Tombor, B., Albert, R., Oltvai, Z., Barabási, A.-L.: The large-scale organization of metabolic networks. Nature 407, 651 (2000)CrossRefGoogle Scholar
  10. 10.
    Lu, L.: The diameter of random massive graphs. In: ACM-SIAM (ed.) 12th Ann. Symp. on Discrete Algorithms (SODA), pp. 912–921 (2001)Google Scholar
  11. 11.
    Monson, S.D., Pullman, N.J., Rees, R.: A survey of clique and biclique coverings and factorizations of (0,1)-matrices. Bull. Inst. Combin. Appl. 14, 17–86 (1995)MATHMathSciNetGoogle Scholar
  12. 12.
    Newman, M.E.J.: Scientific collaboration networks: I. Network construction and fundamental results. Phys. Rev. E 64 (2001)Google Scholar
  13. 13.
    Newman, M.E.J.: The structure and function of complex networks. SIAM Review 45(2), 167–256 (2003)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Newman, M.E.J., Watts, D.J., Strogatz, S.H.: Random graph models of social networks. Proc. Natl. Acad. Sci. USA 99(Suppl.1), 2566–2572 (2002)MATHCrossRefGoogle Scholar
  15. 15.
    Orlin, J.: Contentment in graph theory: Covering graphs with cliques. Indigationes Mathematicae 80, 406–424 (1977)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Bible Today New International Version, http://www.tniv.info/bible/
  17. 17.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393, 440–442 (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jean-Loup Guillaume
    • 1
  • Matthieu Latapy
    • 1
  1. 1.LIAFA – CNRSUniversité Paris 7ParisFrance

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