Abstract
Katz centrality is a fundamental concept to measure the influence of a vertex in a social network. However, existing approaches to calculating Katz centrality in a large-scale network is unpractical and computationally expensive. In this paper, we propose a novel method to estimate Katz centrality based on graph sampling techniques. Specifically, we develop an unbiased estimator for Katz centrality using a multi-round sampling approach. We further propose SAKE, a Sampling based Algorithm for fast Katz centrality Estimation. We prove that the estimator calculated by SAKE is probabilistically guaranteed to be within an additive error from the exact value. The computational complexity of SAKE is much lower than the state-of-the-arts. Extensive evaluation experiments based on four real world networks show that the proposed algorithm achieves low mean relative error with low sampling rate, and it works well in identifying high influence vertices in social networks.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Livemocha network dataset - KONECT, April 2017. http://konect.uni-koblenz.de/networks/livemocha
Ahmed, N.K., Neville, J., Kompella, R.: Network sampling: from static to streaming graphs. ACM Trans. Knowl. Discov. Data (TKDD 2014) 8(2), 7 (2014)
Auer, S., Bizer, C., Kobilarov, G., Lehmann, J., Cyganiak, R., Ives, Z.: DBpedia: a nucleus for a web of open data. In: Aberer, K., et al. (eds.) ASWC/ISWC -2007. LNCS, vol. 4825, pp. 722–735. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-76298-0_52
Balkanski, E., Singer, Y.: Approximation guarantees for adaptive sampling. In: International Conference on Machine Learning (ICML 2018), pp. 393–402 (2018)
Boldi, P., Vigna, S.: Axioms for centrality. Internet Math. 10(3–4), 222–262 (2014)
Bonchi, F., Esfandiar, P., Gleich, D.F., Greif, C., Lakshmanan, L.V.: Fast matrix computations for pairwise and columnwise commute times and Katz scores. Internet Math. 8(1–2), 73–112 (2012)
David, E., Jon, K.: Networks, Crowds, and Markets: Reasoning About a Highly Connected World. Cambridge University Press, New York (2010)
Eden, T., Jain, S., Pinar, A., Ron, D., Seshadhri, C.: Provable and practical approximations for the degree distribution using sublinear graph samples. In: Proceedings of the 27th International Conference on World Wide Web (WWW 2018), pp. 449–458 (2018)
Foster, K.C., Muth, S.Q., Potterat, J.J., Rothenberg, R.B.: A faster Katz status score algorithm. Comput. Math. Organ. Theory 7(4), 275–285 (2001)
Hoeffding, W.: Probability inequalities for sums of bounded random variables. J. Am. Stat. Assoc. 58(301), 13–30 (1963)
Horvitz, D.G., Thompson, D.J.: A generalization of sampling without replacement from a finite universe. J. Am. Stat. Assoc. 47(260), 663–685 (1952)
Katz, L.: A new status index derived from sociometric analysis. Psychometrika 18(1), 39–43 (1953)
Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. In: ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD 2003), pp. 137–146 (2003)
Leskovec, J., Faloutsos, C.: Sampling from large graphs. In: Proceedings of the 12th International Conference on Knowledge Discovery and Data Mining (KDD 2006), pp. 631–636. ACM (2006)
Leskovec, J., Lang, K.J., Dasgupta, A., Mahoney, M.W.: Statistical properties of community structure in large social and information networks. In: Proceedings of the 17th International Conference on World Wide Web, pp. 695–704. ACM (2008)
Maiya, A.S., Berger-Wolf, T.Y.: Benefits of bias: towards better characterization of network sampling. In: Proceedings of the 17th International Conference on Knowledge Discovery and Data Mining (KDD 2011), pp. 105–113. ACM (2011)
Manning, C., Raghavan, P., Schütze, H.: Introduction to information retrieval. Nat. Lang. Eng. 16(1), 100–103 (2010)
Nathan, E., Bader, D.A.: Approximating personalized Katz centrality in dynamic graphs. In: Wyrzykowski, R., Dongarra, J., Deelman, E., Karczewski, K. (eds.) PPAM 2017. LNCS, vol. 10777, pp. 290–302. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78024-5_26
Nathan, E., Sanders, G., Fairbanks, J., Bader, D.A., et al.: Graph ranking guarantees for numerical approximations to Katz centrality. Procedia Comput. Sci. 108, 68–78 (2017)
Riondato, M., Kornaropoulos, E.M.: Fast approximation of betweenness centrality through sampling. Data Min. Knowl. Discov. 30(2), 438–475 (2016)
Riondato, M., Upfal, E.: ABRA: approximating betweenness centrality in static and dynamic graphs with Rademacher averages. ACM Trans. Knowl. Discov. Data (TKDD 2018) 12(5), 61 (2018)
Takac, L., Zabovsky, M.: Data analysis in public social networks. In: International Scientific Conference and International Workshop Present Day Trends of Innovations, vol. 1 (2012)
Wagner, C., Singer, P., Karimi, F., Pfeffer, J., Strohmaier, M.: Sampling from social networks with attributes. In: Proceedings of the 26th International Conference on World Wide Web (WWW 2017), pp. 1181–1190 (2017)
Was, T., Skibski, O.: An axiomatization of the eigenvector and Katz centralities. In: Proceedings of the 32nd AAAI Conference on Artificial Intelligence (AAAI 2018) (2018)
Zhao, J., Yang, T.H., Huang, Y., Holme, P.: Ranking candidate disease genes from gene expression and protein interaction: a Katz-centrality based approach. PLoS ONE 6(9), e24306 (2011)
Acknowledgment
This work was partially supported by the National Key R&D Program of China (Grant No. 2018YFB1004704), the National Natural Science Foundation of China (Grant Nos. 61972196, 61672278, 61832008, 61832005), the Key R&D Program of Jiangsu Province, China (Grant No. BE2018116), the science and technology project from State Grid Corporation of China (Contract No. SGSNXT00YJJS- 1800031), the Collaborative Innovation Center of Novel Software Technology and Industrialization, and the Sino-German Institutes of Social Computing.
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Lin, M., Li, W., Nguyen, Ct., Wang, X., Lu, S. (2020). Sampling Based Katz Centrality Estimation for Large-Scale Social Networks. In: Wen, S., Zomaya, A., Yang, L.T. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2019. Lecture Notes in Computer Science(), vol 11945. Springer, Cham. https://doi.org/10.1007/978-3-030-38961-1_50
Download citation
DOI: https://doi.org/10.1007/978-3-030-38961-1_50
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-38960-4
Online ISBN: 978-3-030-38961-1
eBook Packages: Computer ScienceComputer Science (R0)