Quick Detection of Nodes with Large Degrees

  • Konstantin Avrachenkov
  • Nelly Litvak
  • Marina Sokol
  • Don Towsley
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7323)


Our goal is to quickly find top k lists of nodes with the largest degrees in large complex networks. If the adjacency list of the network is known (not often the case in complex networks), a deterministic algorithm to find the top k list of nodes with the largest degrees requires an average complexity of \(\mbox{O}(n)\), where n is the number of nodes in the network. Even this modest complexity can be very high for large complex networks. We propose to use the random walk based method. We show theoretically and by numerical experiments that for large networks the random walk method finds good quality top lists of nodes with high probability and with computational savings of orders of magnitude. We also propose stopping criteria for the random walk method which requires very little knowledge about the structure of the network.

Õ(n 2)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Avrachenkov, K., Ribeiro, B., Towsley, D.: Improving Random Walk Estimation Accuracy with Uniform Restarts. In: Kumar, R., Sivakumar, D. (eds.) WAW 2010. LNCS, vol. 6516, pp. 98–109. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  2. 2.
    Avrachenkov, K., Borkar, V., Nemirovsky, D.: Quasi-stationary distributions as centrality measures for the giant strongly connected component of a reducible graph. Journal of Comp. and Appl. Mathematics 234, 3075–3090 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Avrachenkov, K., Litvak, N., Nemirovsky, D., Smirnova, E., Sokol, M.: Quick Detection of Top-k Personalized PageRank Lists. In: Frieze, A., Horn, P., Prałat, P. (eds.) WAW 2011. LNCS, vol. 6732, pp. 50–61. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  4. 4.
    Boldi, P., Vigna, S.: The WebGraph framework I: Compression techniques. In: Proceedings of WWW 2004 (2004)Google Scholar
  5. 5.
    Boldi, P., Rosa, M., Santini, M., Vigna, S.: Layered label propagation: A multiresolution coordinate-free ordering for compressing social networks. In: Proceedings of WWW 2011 (2011)Google Scholar
  6. 6.
    Dorogovtsev, S.N., Mendes, J.F.F., Samukhin, A.N.: Structure of growing networks: Exact solution of the Barabasi-Albert model. Phys. Rev. Lett. 85, 4633–4636 (2000)CrossRefGoogle Scholar
  7. 7.
    van der Hofstad, R.: Random graphs and complex networks. Lecture Notes (2009),
  8. 8.
    Lim, Y., Menasche, D.S., Ribeiro, B., Towsley, D., Basu, P.: Online estimating the k central nodes of a network. In: Proceedings of IEEE NSW 2011 (2011)Google Scholar
  9. 9.
    Maiya, A.S., Berger-Wolf, T.Y.: Online Sampling of High Centrality Individuals in Social Networks. In: Zaki, M.J., Yu, J.X., Ravindran, B., Pudi, V. (eds.) PAKDD 2010, Part I. LNCS, vol. 6118, pp. 91–98. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  10. 10.
    Moreira, A.A., Andrade Jr., J.S., Amaral, L.A.N.: Extremum statistics in scale-free network models. Phys. Rev. Lett. 89, 268703, 4 pages (2002)Google Scholar
  11. 11.
    Matthys, G., Beirlant, J.: Estimating the extreme value index and high quantiles with exponential regression models. Statistica Sinica 13(3), 853–880 (2003)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Mitzenmacher, M., Upfal, E.: Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge University Press (2005)Google Scholar
  13. 13.
    Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge University Press (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Konstantin Avrachenkov
    • 1
  • Nelly Litvak
    • 2
  • Marina Sokol
    • 1
  • Don Towsley
    • 3
  1. 1.INRIASophia-AntipolisFrance
  2. 2.University of TwenteThe Netherlands
  3. 3.University of MassachusettsAmherstUSA

Personalised recommendations