Toward Identity Anonymization in Social Networks

  • Kenneth L. Clarkson
  • Kun Liu
  • Evimaria Terzi


The proliferation of network data in various application domains has raised privacy concerns for the individuals involved. Recent studies show that simply removing the identities of the nodes before publishing the graph/social network data does not guarantee privacy. The structure of the graph itself, and in its basic form the degree of the nodes, can be revealing the identities of individuals. To address this issue, we study a specific graph-anonymization problem. We call a graph k-degree anonymous if for every node v, there exist at least k-1 other nodes in the graph with the same degree as v. This definition of anonymity prevents the re-identification of individuals by adversaries with a priori knowledge of the degree of certain nodes. We formally define the graph-anonymization problem that, given a graph G, asks for the k-degree anonymous graph that stems from G with the minimum number of graph-modification operations. We devise simple and efficient algorithms for solving this problem. Our algorithms are based on principles related to the realizability of degree sequences. We apply our methods to a large spectrum of synthetic and real data sets and demonstrate their efficiency and practical utility.


Original Graph Input Graph Average Path Length Degree Sequence Edge Addition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    C. C. Aggarwal, and P. S. Yu. Privacy-Preserving Data Mining: Models and Algorithms, vol. 34 of Advances in Database Systems. Springer, 233 Spring Street, New York, NY 10013, USA, 2008.Google Scholar
  2. 2.
    L. Backstrom, C. Dwork, and J. M. Kleinberg. Wherefore art thou R3579X?: Anonymized social networks, hidden patterns, and structural steganography. In Proceedings of the 16th International Conference on World Wide Web (WWW’07) (Alberta, Canada, May 2007), pp. 181–190.Google Scholar
  3. 3.
    A.-L. Barabási, and R. Albert. Emergence of scaling in random networks. Science 286, 5439 (October 1999), 509–512.Google Scholar
  4. 4.
    R. J. Bayardo, and R. Agrawal. Data privacy through optimal k-anonymization. In Proceedings of the 21st International Conference on Data Engineering (ICDE’05), pages 217–228 Tokyo, Japan, April 2005.Google Scholar
  5. 5.
    S. Boyd, and L. Vandenberghe. Convex Optimization. Cambridge University Press, Cambridge, 2004.Google Scholar
  6. 6.
    T. Cormen, C. Leiserson, and R. Rivest. Introduction to Algorithms. MIT Press, Cambridge, MA, 1990.Google Scholar
  7. 7.
    I. Diakonikolas, and M. Yannakakis. Succinct approximate convex pareto curves. In SODA, pages 74–83 2008.Google Scholar
  8. 8.
    P. Erdös, and T. Gallai. Graphs with prescribed degrees of vertices. Mat. Lapok, 11:264–274, 1960.Google Scholar
  9. 9.
    L. Getoor, and C. P. Diehl. Link mining: a survey. ACM SIGKDD Explorations Newsletter, 7, (2): 3–12, 2005.CrossRefGoogle Scholar
  10. 10.
    S. L. Hakimi. On realizability of a set of integers as degrees of the vertices of a linear graph. Journal of the Society for Industrial and Applied Mathematics, 10(3): 496–506, 1962.CrossRefGoogle Scholar
  11. 11.
    M. Hay, G. Miklau, D. Jensen, D. Towsely, and P. Weis. Resisting structural re-identification in anonymized social networks. In Proceedings of the VLDB Endowment. Volume 1, Issue 1, pages 102–114, Publisher VLDB Endowment, August 2008.Google Scholar
  12. 12.
    M. Hay, G. Miklau, D. Jensen, P. Weis, and S. Srivastava. Anonymizing social networks. Technical report, University of Massachusetts Amherst, 2007.Google Scholar
  13. 13.
    A. Korolova, R. Motwani, S. U. Nabar, and 0002, Y. X. Link privacy in social networks. In CIKM, pages 289–298, 2008.Google Scholar
  14. 14.
    Y.-S. Lee. Graphical demonstration of an optimality property of the median. The American Statistician 49(4): 369–372, November 1995.Google Scholar
  15. 15.
    K. Liu, and E. Terzi. Towards identity anonymization on graphs. In Proceedings of the 2008 ACM SIGMOD International Conference on Management of Data (SIGMOD’08), pages 93–106, Vancouver, Canada, June 2008.Google Scholar
  16. 16.
    A. Machanavajjhala, J. Gehrke, D. Kifer, and M. Venkitasubramaniam. l-diversity: Privacy beyond k-anonymity. In Proceedings of the 22nd International Conference on Data Engineering (ICDE’06), pages 24, Atlanta, GA, April 2006, 2006.Google Scholar
  17. 17.
    A. Meyerson, and R. Williams. On the complexity of optimal k-anonymity. In Proceedings of the Twenty-third ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems (PODS’04), pages 223–228, Paris, France, 2004, 2004.Google Scholar
  18. 18.
    J. Pei, and B. Zhou. Preserving privacy in social networks against neighborhood attacks. In Proceedings of the 24th International Conference on Data Engineering (ICDE’08), Cancun, Mexico, April 2008.Google Scholar
  19. 19.
    P. Samarati, and L. Sweeney. Generalizing data to provide anonymity when disclosing information. In Proceedings of the Seventeenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS’98) page 188 Seattle, WA, 1998.Google Scholar
  20. 20.
    D. J. Watts. Networks, dynamics, and the small-world phenomenon. American Journal of Sociology, 105(2): 493–527, September 1999.CrossRefGoogle Scholar
  21. 21.
    D. J. Watts, and S. H. Strogatz. Collective dynamics of small-world networks. Nature 393 (6684): 409–410, June 1998.CrossRefGoogle Scholar
  22. 22.
    X. Ying, and X. Wu. Randomizing social networks: a spectrum preserving approach. In Proceedings of SIAM International Conference on Data Mining (SDM’08), pages 739–750, Atlanta, GA, April 2008.Google Scholar
  23. 23.
    E. Zheleva, and L. Getoor. Preserving the privacy of sensitive relationships in graph data. In Proceedings of the International Workshop on Privacy, Security, and Trust in KDD (PinKDD’07), pages 153–171, San Jose, CA, August 2007.Google Scholar
  24. 24.
    B. Zhou, J. Pei, and W.-S. Luk. A brief survey on anonymization techniques for privacy preserving publishing of social network data. ACM SIGKDD Explorations 10(2): 12–22, December, 2008.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.IBM Almaden Research CenterSan JoseUSA
  2. 2.Yahoo! LabsSanta ClaraUSA
  3. 3.Computer Science DepartmentBoston UniversityBostonUSA

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