Fast Generation of Scale Free Networks with Directed Arcs

  • Huqiu Zhang
  • Aad van Moorsel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5652)

Abstract

To evaluate peer-to-peer systems through discrete-event simulation, one needs to be able to generate sufficiently large networks of nodes that exhibit the desired properties, such as the scale-free nature of the connectivity graph. In applications such as the web of trust or analysis of hyperlink structures, the direction of the arcs between two nodes is relevant and one therefore generates directed graphs. In this paper we introduce a model to generate directed scale free graphs without multiple arcs between the same pair of nodes and loops. This model is based on existing models that allows multiple arcs and loops, but considerably more challenging to implement in an efficient manner. We therefore design and implement a set of algorithms and compare them with respect to CPU and memory use, in terms of both theoretical complexity analysis and experimental results. We will show through experiments that with the fastest algorithms networks with a million or more nodes can be generated in mere seconds.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Lv, Q., Cao, P., Cohen, E., Li, K., Shenker, S.: Search and replication in unstructured peer-to-peer networks. In: ICS 2002: Proceedings of the 16th International Conference on Supercomputing, pp. 84–95. ACM Press, New York (2002)Google Scholar
  2. 2.
    Ribeiro de Mello, E., van Moorsel, A.P.A., da Silva Fraga, J.: Evaluation of P2P search algorithms for discovering trust paths. In: European Performance Engineering Workshop, pp. 112–124 (2007)Google Scholar
  3. 3.
    Zhang, H., van Moorsel, A.P.A.: Evaluation of P2P algorithms for probabilistic trust inference in a web of trust. In: Thomas, N., Juiz, C. (eds.) EPEW 2008. LNCS, vol. 5261, pp. 242–256. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Newman, M.E.J.: Power laws, Pareto+ distributions and Zipf’s law. Contemporary Physics 46(323) (2005)Google Scholar
  5. 5.
    Caldarelli, G.: Scale-Free Networks: Complex Webs in Nature and Technology. Oxford University Press, Oxford (2007)CrossRefMATHGoogle Scholar
  6. 6.
    Albert, R., Barabási, A.: Statistical mechanics of complex networks. Reviews of Modern Physics 74 (2002)Google Scholar
  7. 7.
    Bollobás, B., Borgs, C., Chayes, J., Riordan, O.: Directed scale-free graphs. In: SODA 2003: Proceedings of the Fourteenth Annual ACM–SIAM Symposium on Discrete Algorithms, pp. 132–139 (2003)Google Scholar
  8. 8.
    Krapivsky, P.L., Rodgers, G.J., Redner, S.: Degree distributions of growing networks. Physical Review Letters 86, 5401 (2001)CrossRefGoogle Scholar
  9. 9.
    Efraimidis, P.S., Spirakis, P.G.: Weighted random sampling with a reservoir. Inf. Process. Lett., 181–185 (2006)Google Scholar
  10. 10.
    Barabasi, A.L., Albert, R.: Emergence of scaling in random networks. Science 286, 509 (1999)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Jesi, G.P.: Peersim: A peer-to-peer simulator (2004), http://peersim.sourceforge.net
  12. 12.
    Broder, A., Kumar, R., Maghoul, F., Raghavan, P., Rajagopalan, S., Stata, R., Tomkins, A., Wiener, J.: Graph structure in the web. Comput. Netw. 33(1-6), 309–320 (2000)CrossRefGoogle Scholar
  13. 13.
    jimt: Efficiently selecting a random, weighted element, http://www.perlmonks.org/?node_id=577433

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Huqiu Zhang
    • 1
  • Aad van Moorsel
    • 1
  1. 1.School of Computing ScienceNewcastle University, Newcastle upon TyneUK

Personalised recommendations