Fast Identity Anonymization on Graphs

  • Xuesong Lu
  • Yi Song
  • Stéphane Bressan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7446)


Liu and Terzi proposed the notion of k-degree anonymity to address the problem of identity anonymization in graphs. A graph is k-degree anonymous if and only if each of its vertices has the same degree as that of, at least, k-1 other vertices. The anonymization problem is to transform a non-k-degree anonymous graph into a k-degree anonymous graph by adding or deleting a minimum number of edges.

Liu and Terzi proposed an algorithm that remains a reference for k-degree anonymization. The algorithm consists of two phases. The first phase anonymizes the degree sequence of the original graph. The second phase constructs a k-degree anonymous graph with the anonymized degree sequence by adding edges to the original graph. In this work, we propose a greedy algorithm that anonymizes the original graph by simultaneously adding edges to the original graph and anonymizing its degree sequence. We thereby avoid testing the realizability of the degree sequence, which is a time consuming operation. We empirically and comparatively evaluate our new algorithm. The experimental results show that our algorithm is indeed more efficient and more effective than the algorithm proposed by Liu and Terzi on large real graphs.


Edit Distance Original Graph Degree Sequence Average Short Path Length Residual Degree 
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.


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  1. 1.
    Backstrom, L., Dwork, C., Kleinberg, J.M.: Wherefore art thou R3579X?: Anonymized social networks, hidden patterns, and structural steganography. Commun. ACM 54(12) (2011)Google Scholar
  2. 2.
    Barabási, A.-L., Albert, R.: Emergence of Scaling in Random Networks. Science 286, 509–512 (1999)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bhagat, S., Cormode, G., Krishnamurthy, B., Srivastava, D.: Class-based graph anonymization for social network data. PVLDB 2(1) (2009)Google Scholar
  4. 4.
    Campan, A., Truta, T.M.: A clustering approach for data and structural anonymity in social networks. In: PinKDD (2008)Google Scholar
  5. 5.
    Cheng, J., Fu, A.W.-C., Liu, J.: K-isomorphism: privacy-preserving network publication against structural attacks. In: SIGMOD (2010)Google Scholar
  6. 6.
    Clauset, A., Shalizi, C.R., Newman, M.E.J.: Power-law distributions in empirical data. SIAM Reviews (2007)Google Scholar
  7. 7.
    Cormode, G., Srivastava, D., Yu, T., Zhang, Q.: Anonymizing bipartite graph data using safe groupings. PVLDB 19(1) (2010)Google Scholar
  8. 8.
    Francesco Bonchi, A.G., Tassa, T.: Identity obfuscation in graphs through the information theoretic lens. In: ICDE (2011)Google Scholar
  9. 9.
    Ghinita, G., Karras, P., Kalnis, P., Mamoulis, N.: Fast data anonymization with low information loss. In: VLDB, pp. 758–769 (2007)Google Scholar
  10. 10.
    Hay, M., Miklau, G., Jensen, D., Towsley, D., Weis, P.: Resisting structural re-identification in anonymized social networks. PVLDB 1(1), 102–114 (2008)Google Scholar
  11. 11.
    Korolova, A., Motwani, R., Nabar, S.U., Xu, Y.: Link privacy in social networks. In: CIKM (2008)Google Scholar
  12. 12.
    Li, Y., Shen, H.: Anonymizing graphs against weight-based attacks. In: ICDM Workshops (2010)Google Scholar
  13. 13.
    Liu, K., Terzi, E.: Towards identity anonymization on graphs. In: SIGMOD Conference, pp. 93–106 (2008)Google Scholar
  14. 14.
    Liu, L., Wang, J., Liu, J., Zhang, J.: Privacy preserving in social networks against sensitive edge disclosure. In: SIAM International Conference on Data Mining (2009)Google Scholar
  15. 15.
    Song, Y., Nobari, S., Lu, X., Karras, P., Bressan, S.: On the privacy and utility of anonymized social networks. In: iiWAS (2011)Google Scholar
  16. 16.
    Sweeney, L.: K-anonymity: a model for protecting privacy. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 10(5) (2002)Google Scholar
  17. 17.
    Tai, C.-H., Yu, P.S., Yang, D.-N., Chen, M.-S.: Privacy-preserving social network publication against friendship attacks. In: SIGKDD (2011)Google Scholar
  18. 18.
    Wu, W., Xiao, Y., Wang, W., He, Z., Wang, Z.: K-symmetry model for identity anonymization in social networks. In: EDBT (2010)Google Scholar
  19. 19.
    Ying, X., Wu, X.: Randomizing social networks: a spectrum perserving approach. In: SDM (2008)Google Scholar
  20. 20.
    Yuan, M., Chen, L., Yu, P.S.: Personalized privacy protection in social networks. PVLDB 4(2) (2010)Google Scholar
  21. 21.
    Zheleva, E., Getoor, L.: Preserving the Privacy of Sensitive Relationships in Graph Data. In: Bonchi, F., Malin, B., Saygın, Y. (eds.) PInKDD 2007. LNCS, vol. 4890, pp. 153–171. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  22. 22.
    Zhou, B., Pei, J.: Preserving privacy in social networks against neighborhood attacks. In: ICDE (2008)Google Scholar
  23. 23.
    Zou, L., Chen, L., Özsu, M.T.: K-automorphism: a general framework for privacy-preserving network publication. PVLDB 2(1) (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Xuesong Lu
    • 1
  • Yi Song
    • 1
  • Stéphane Bressan
    • 1
  1. 1.School of ComputingNational University of SingaporeSingapore

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