Estimating the Degrees of Neighboring Nodes in Online Social Networks

  • Jooyoung Lee
  • Jae C. Oh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8861)


We propose an agent centric algorithm that each agent (i.e., node) in a social network can use to estimate each of its neighbor’s degree. The knowledge about the degrees of neighboring nodes is useful for many existing algorithms in social networks studies. For example, algorithms to estimate the diffusion rate of information spread need such information. In many studies, either such degree information is assumed to be available or an overall probabilistic distribution of degrees of nodes is presumed. Furthermore, most of these existing algorithms facilitate a macro-level analysis assuming the entire network is available to the researcher although sampling may be required due to the size of the network. In this paper, we consider the case that the network topology is unknown to individual nodes and therefore each node must estimate the degrees of its neighbors. In estimating the degrees, the algorithm correlates observable activities of neighbors to Bernoulli trials and utilize a power-law distribution to infer unobservable activities. Our algorithm was able to estimate the neighbors’ degrees in 92% accuracy for the 60867 number of nodes. We evaluate the mean squared error of accuracy for the proposed algorithm on a real and a synthetic networks.


Online social networks degree estimations distributed computation 


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  1. 1.
    Hay, M., Li, C., Miklau, G., Jensen, D.: Accurate estimation of the degree distribution of private networks. In: Proceedings of the 2009 Ninth IEEE International Conference on Data Mining, ICDM 2009, pp. 169–178. IEEE Computer Society, Washington, DC (2009)Google Scholar
  2. 2.
    Snijders, T.A.B.: Accounting for degree distributions in empirical analysis of network dynamics. Proceedings of the National Academy of Sciences, 109–114 (2003)Google Scholar
  3. 3.
    Kupavskii, A., Ostroumova, L., Shabanov, D.A., Tetali, P.: The distribution of second degrees in the buckley-osthus random graph model. Internet Mathematics 9(4), 297–335 (2013)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Wang, T., Chen, Y., Zhang, Z., Xu, T., Jin, L., Hui, P., Deng, B., Li, X.: Understanding graph sampling algorithms for social network analysis. In: ICDCS Workshops, pp. 123–128. IEEE Computer Society (2011)Google Scholar
  5. 5.
    Ribeiro, B.F., Towsley, D.: On the estimation accuracy of degree distributions from graph sampling. In: CDC, pp. 5240–5247 (2012)Google Scholar
  6. 6.
    Lee, J.Y., Oh, J.C.: A model for recursive propagations of reputations in social networks. In: Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, ASONAM 2013, pp. 666–670. ACM, New York (2013)CrossRefGoogle Scholar
  7. 7.
    Lenzen, C., Wattenhofer, R.: Distributed Algorithms for Sensor Networks. Philosophical Transactions of the Royal Society A 370(1958) (January 2012)Google Scholar
  8. 8.
    Albert, R., Barabási, A.L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74(1), 47–97 (2002)CrossRefzbMATHGoogle Scholar
  9. 9.
    Ribeiro, B.F., Towsley, D.: On the estimation accuracy of degree distributions from graph sampling. In: CDC, pp. 5240–5247 (2012)Google Scholar
  10. 10.
    Ye, S., Wu, S.F.: Estimating the size of online social networks. In: Elmagarmid, A.K., Agrawal, D. (eds.) SocialCom/PASSAT, pp. 169–176. IEEE Computer Society (2010)Google Scholar
  11. 11.
    Page, L., Brin, S., Motwani, R., Winograd, T.: The pagerank citation ranking: Bringing order to the web. Technical Report 1999-66, Stanford InfoLab (November 1999)Google Scholar
  12. 12.
    Mislove, A., Marcon, M., Gummadi, K.P., Druschel, P., Bhattacharjee, B.: Measurement and analysis of online social networks. In: Proceedings of the 7th ACM SIGCOMM Conference on Internet Measurement, IMC 2007, pp. 29–42. ACM, New York (2007)Google Scholar
  13. 13.
    Erdös, P., Rényi, A.: On random graphs, I. Publicationes Mathematicae (Debrecen) 6, 290–297 (1959)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Galeotti, A., Goyal, S., Jackson, M.O., Vega-Redondo, F., Yariv, L.: Network games. Review of Economic Studies 77(1), 218–244 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Casella, G., Berger, R.: Statistical Inference. Duxbury Resource Center (June 2001)Google Scholar
  16. 16.
    Csanyi, G., Szendroi, B.: Structure of a large social network. Physical Review E 69(3) (March 2004); 036131 PT: J; PN: Part 2; PG: 5Google Scholar
  17. 17.
    Shannon, P., Markiel, A., Ozier, O., Baliga, N.S., Wang, J.T., Ramage, D., Amin, N., Schwikowski, B., Ideker, T.: Cytoscape: a software environment for integrated models of biomolecular interaction networks. Genome Research 13(11), 2498–2504 (2003)CrossRefGoogle Scholar
  18. 18.
    Viswanath, B., Mislove, A., Cha, M., Gummadi, K.P.: On the evolution of user interaction in facebook. In: Proceedings of the 2nd ACM SIGCOMM Workshop on Social Networks (WOSN 2009) (August 2009)Google Scholar
  19. 19.
    Mislove, A., Marcon, M., Gummadi, K.P., Druschel, P., Bhattacharjee, B.: Measurement and analysis of online social networks. In: Proceedings of the 5th ACM/USENIX Internet Measurement Conference (IMC 2007) (2007)Google Scholar
  20. 20.
    Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69(2), 026113 (2004)Google Scholar
  21. 21.
    Clauset, A., Shalizi, C.R., Newman, M.E.J.: Power-law distributions in empirical data. SIAM Rev. 51(4), 661–703 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Gillespie, C.S.: Fitting heavy tailed distributions: the poweRlaw package (2014), R package version 0.20.5Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Jooyoung Lee
    • 1
  • Jae C. Oh
    • 2
  1. 1.Innopolis UniversityKazanRussia
  2. 2.Department of Electrical Engineering and Computer ScienceSyracuse UniversitySyracuseUSA

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