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Sampling on Networks: Estimating Eigenvector Centrality on Incomplete Networks

Part of the Studies in Computational Intelligence book series (SCI,volume 881)

Abstract

We develop a new sampling method to estimate eigenvector centrality on incomplete networks. Our goal is to estimate this global centrality measure having at disposal a limited amount of data. This is the case in many real-world scenarios where data collection is expensive, the network is too big for data storage capacity or only partial information is available. The sampling algorithm is theoretically grounded by results derived from spectral approximation theory. We studied the problem on both synthetic and real data and tested the performance comparing with state-of-the-art methods. We show that approximations obtained from such methods are not always reliable and that our algorithm, while preserving computational scalability, improves performance under some relevant error measures.

Keywords

  • Sampling
  • Networks
  • Eigenvector centrality

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Fig. 1.
Fig. 2.

Notes

  1. 1.

    http://irl.cs.ucla.edu/topology/.

  2. 2.

    https://snap.stanford.edu/data/ca-CondMat.html.

  3. 3.

    https://snap.stanford.edu/data/soc-Epinions1.html.

  4. 4.

    https://snap.stanford.edu/data/web-Stanford.html.

  5. 5.

    https://github.com/cdebacco/tcec_sampling.

References

  1. De Choudhury, M., Lin, Y.R., Sundaram, H., Candan, K.S., Xie, L., Kelliher, A.: How does the data sampling strategy impact the discovery of information diffusion in social media?. In: Fourth International AAAI Conference on Weblogs and Social Media (2010)

    Google Scholar 

  2. Sadikov, E., Medina, M., Leskovec, J., Garcia-Molina, H.: Correcting for missing data in information cascades. In: Proceedings of the Fourth ACM International Conference on Web Search and Data Mining, pp. 55–64. ACM (2011)

    Google Scholar 

  3. Leskovec, J., Faloutsos, C.: Sampling from large graphs. In: Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 631–636. ACM (2006)

    Google Scholar 

  4. Adler, M., Mitzenmacher, M.: Towards compressing web graphs. In: Data Compression Conference Proceedings DCC 2001, pp. 203–212. IEEE (2001)

    Google Scholar 

  5. Frank, O.: Network sampling and model fitting. In: Models and Methods in Social Network Analysis, pp. 31–56 (2005)

    Google Scholar 

  6. Han, J.-D.J., Dupuy, D., Bertin, N., Cusick, M.E., Vidal, M.: Effect of sampling on topology predictions of protein-protein interaction networks. Nat. Biotechnol. 23(7), 839 (2005)

    CrossRef  Google Scholar 

  7. Lee, S.H., Kim, P.-J., Jeong, H.: Statistical properties of sampled networks. Phys. Rev. E 73(1), 016102 (2006)

    CrossRef  Google Scholar 

  8. Kossinets, G.: Effects of missing data in social networks. Soc. Netw. 28(3), 247–268 (2006)

    CrossRef  Google Scholar 

  9. Bonacich, P.: Factoring and weighting approaches to status scores and clique identification. J. Math. Sociol. 2(1), 113–120 (1972)

    CrossRef  Google Scholar 

  10. Costenbader, E., Valente, T.W.: The stability of centrality measures when networks are sampled. Soc. Netw. 25(4), 283–307 (2003)

    CrossRef  Google Scholar 

  11. Saad, Y.: Numerical Methods for Large Eigenvalues Problems. Manchester University Press, Manchester (2011)

    CrossRef  Google Scholar 

  12. Blagus, N., Šubelj, L., Bajec, M.: Empirical comparison of network sampling: how to choose the most appropriate method? Physica A: Stat. Mech. Appl. 477, 136–148 (2017)

    CrossRef  Google Scholar 

  13. Morstatter, F., Pfeffer, J., Liu, H., Carley, K.M.: Is the sample good enough? comparing data from Twitter’s streaming API with Twitter’s firehose. In: Seventh International AAAI Conference on Weblogs and Social Media (2013)

    Google Scholar 

  14. Stutzbach, D., Rejaie, R., Duffield, N., Sen, S., Willinger, W.: On unbiased sampling for unstructured peer-to-peer networks. IEEE/ACM Trans. Netw. (TON) 17(2), 377–390 (2009)

    CrossRef  Google Scholar 

  15. Hübler, C., Kriegel, H.-P., Borgwardt, K., Ghahramani, Z.: Metropolis algorithms for representative subgraph sampling. In: 2008 Eighth IEEE International Conference on Data Mining, pp. 283–292. IEEE (2008)

    Google Scholar 

  16. Stumpf, M.P., Wiuf, C.: Sampling properties of random graphs: the degree distribution. Phys. Rev. E 72(3), 036118 (2005)

    MathSciNet  CrossRef  Google Scholar 

  17. Ganguly, A., Kolaczyk, E.D.: Estimation of vertex degrees in a sampled network. In: 2017 51st Asilomar Conference on Signals, Systems, and Computers, pp. 967–974. IEEE (2018)

    Google Scholar 

  18. Antunes, N., Bhamidi, S., Guo, T., Pipiras, V., Wang, B.: Sampling-based estimation of in-degree distribution with applications to directed complex networks. arXiv preprint arXiv:1810.01300 (2018)

  19. Segarra, S., Ribeiro, A.: Stability and continuity of centrality measures in weighted graphs. IEEE Trans. Signal Process. 64(3), 543–555 (2015)

    MathSciNet  CrossRef  Google Scholar 

  20. Han, C.-G., Lee, S.-H.: Analysis of effect of an additional edge on eigenvector centrality of graph. J. Korea Soc. Comput. Inf. 21(1), 25–31 (2016)

    MathSciNet  CrossRef  Google Scholar 

  21. Murai, S., Yoshida, Y.: Sensitivity analysis of centralities on unweighted networks. In: The World Wide Web Conference, pp. 1332–1342. ACM (2019)

    Google Scholar 

  22. Brin, S., Page, L.: The anatomy of a large-scale hypertextual web search engine. Comput. Netw. ISDN Syst. 30(1–7), 107–117 (1998)

    CrossRef  Google Scholar 

  23. Sakakura, Y., Yamaguchi, Y., Amagasa, T., Kitagawa, H.: An improved method for efficient PageRank estimation. In: International Conference on Database and Expert Systems Applications, pp. 208–222. Springer (2014)

    Google Scholar 

  24. Chen, Y.-Y., Gan, Q., Suel, T.: Local methods for estimating PageRank values. In: Proceedings of the Thirteenth ACM International Conference on Information and Knowledge Management, pp. 381–389. ACM (2004)

    Google Scholar 

  25. Golub, G.H., Van Loan, C.F.: Matrix Computations, vol. 3. JHU Press, Baltimore (2012)

    MATH  Google Scholar 

  26. Gjoka, M., Kurant, M., Butts, C.T., Markopoulou, A.: Walking in Facebook: a case study of unbiased sampling of OSNs. In: 2010 Proceedings IEEE Infocom, pp. 1–9. IEEE (2010)

    Google Scholar 

  27. Romance, M.: Local estimates for eigenvector-like centralities of complex networks. J. Comput. Appl. Math. 235(7), 1868–1874 (2011)

    MathSciNet  CrossRef  Google Scholar 

  28. Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)

    MathSciNet  CrossRef  Google Scholar 

  29. Karrer, B., Newman, M.E.: Stochastic blockmodels and community structure in networks. Phys. Rev. E 83(1), 016107 (2011)

    MathSciNet  CrossRef  Google Scholar 

  30. Erdös, P., Rényi, A.: On random graphs, I. Publicationes Mathematicae (Debrecen) 6, 290–297 (1959)

    MathSciNet  MATH  Google Scholar 

  31. Oliveira, R., Willinger, W., Zhang, B., et al.: Quantifying the completeness of the observed internet as-level structure. Work 11(15), 13–17 (2008)

    Google Scholar 

  32. Leskovec, J., Kleinberg, J., Faloutsos, C.: Graph evolution: Densification and shrinking diameters. ACM Trans. Knowl. Discov. Data (TKDD) 1(1), 2 (2007)

    CrossRef  Google Scholar 

  33. Richardson, M., Agrawal, R., Domingos, P.: Trust management for the semantic web. In: International Semantic Web Conference, pp. 351–368. Springer (2003)

    Google Scholar 

  34. Leskovec, J., Lang, K.J., Dasgupta, A., Mahoney, M.W.: Community structure in large networks: natural cluster sizes and the absence of large well-defined clusters. Internet Math. 6(1), 29–123 (2009)

    MathSciNet  CrossRef  Google Scholar 

  35. Maiya, A.S., Berger-Wolf, T.Y.: Sampling community structure. In: Proceedings of the 19th International Conference on World Wide Web, pp. 701–710. ACM (2010)

    Google Scholar 

  36. Lovász, L., et al.: Random walks on graphs: a survey. Comb. Paul Erdos Eighty 2(1), 1–46 (1993)

    Google Scholar 

  37. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equation of state calculations by fast computing machines. J. Chem. Phys. 21(6), 1087–1092 (1953)

    CrossRef  Google Scholar 

  38. Goodman, L.A.: Snowball sampling. Ann. Math. Stat. 32, 148–170 (1961)

    MathSciNet  CrossRef  Google Scholar 

  39. Corder, G.W., Foreman, D.I.: Nonparametric Statistics: A Step-by-Step Approach. Wiley, Hoboken (2014)

    MATH  Google Scholar 

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Correspondence to Caterina De Bacco .

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Ruggeri, N., De Bacco, C. (2020). Sampling on Networks: Estimating Eigenvector Centrality on Incomplete Networks. In: Cherifi, H., Gaito, S., Mendes, J., Moro, E., Rocha, L. (eds) Complex Networks and Their Applications VIII. COMPLEX NETWORKS 2019. Studies in Computational Intelligence, vol 881. Springer, Cham. https://doi.org/10.1007/978-3-030-36687-2_8

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