Classifying Graphs Using Theoretical Metrics: A Study of Feasibility

  • Linhong Zhu
  • Wee Keong Ng
  • Shuguo Han
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6637)


Graph classification has become an increasingly important research topic in recent years due to its wide applications. However, one interesting problem about how to classify graphs based on the implicit properties of graphs has not been studied yet. To address it, this paper first conducts an extensive study on existing graph theoretical metrics and also propose various novel metrics to discover implicit graph properties. We then apply feature selection techniques to discover a subset of discriminative metrics by considering domain knowledge. Two classifiers are proposed to classify the graphs based on the subset of features. The feasibility of graph classification based on the proposed graph metrics and techniques has been experimentally studied.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Agrawal, R., Borgida, A., Jagadish, H.V.: Efficient management of transitive relationships in large data and knowledge bases. In: Proceedings of the 1989 ACM International Conference on Management of Data, pp. 253–262. ACM, New York (1989)Google Scholar
  2. 2.
    Babai, L., Luks, E.M.: Canonical labeling of graphs. In: Proceedings of the 15th Annual ACM Symposium on Theory of Computing, pp. 171–183. ACM, New York (1983)Google Scholar
  3. 3.
    Bunke, H.: On a relation between graph edit distance and maximum common subgraph. Pattern Recognition Letters 18(9), 689–694 (1997)CrossRefGoogle Scholar
  4. 4.
    Cheng, J., Yu, J.X., Lin, X., Wang, H., Yu, P.S.: Fast computation of reachability labeling for large graphs. In: Ioannidis, Y., Scholl, M.H., Schmidt, J.W., Matthes, F., Hatzopoulos, M., Böhm, K., Kemper, A., Grust, T., Böhm, C. (eds.) EDBT 2006. LNCS, vol. 3896, pp. 961–979. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. 5.
    Coffman, T.R., Marcus, S.E.: Dynamic classification of groups through social network analysis and hmms. In: IEEE Aerospace Conference, pp. 3197–3205 (2004)Google Scholar
  6. 6.
    Deshpande, M., Kuramochi, M., Wale, N., Karypis, G.: Frequent substructure-based approaches for classifying chemical compounds. IEEE Transaction on Knowledge and Data Engineering 17(8), 1036–1050 (2005)CrossRefGoogle Scholar
  7. 7.
    Diestel, R.: Graph Theory, 3rd edn., vol. 173. Springer, Heidelberg (2005)zbMATHGoogle Scholar
  8. 8.
    Faloutsos, M., Yang, Q., Siganos, G., Lonardi, S.: Evolution versus intelligent design: comparing the topology of protein-protein interaction networks to the internet. In: Proceedings of the LSS Computational Systems Bioinformatics Conference, Stanford, CA, pp. 299–310 (2006)Google Scholar
  9. 9.
    Montes-y-Gómez, M., López-López, A., Gelbukh, A.: Information retrieval with conceptual graph matching. In: Ibrahim, M., Küng, J., Revell, N. (eds.) DEXA 2000. LNCS, vol. 1873, pp. 312–321. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  10. 10.
    Jin, N., Young, C., Wang, W.: Graph classification based on pattern co-occurrence. In: Proceeding of the 18th ACM Conference on Information and Knowledge Management, pp. 573–582. ACM, New York (2009)Google Scholar
  11. 11.
    Jin, N., Young, C., Wang, W.: Gaia: graph classification using evolutionary computation. In: Proceedings of the 2010 International Conference on Management of Data, pp. 879–890. ACM, New York (2010)Google Scholar
  12. 12.
    Kong, X., Yu, P.S.: Semi-supervised feature selection for graph classification. In: Proceedings of the 16th ACM International Conference on Knowledge Discovery and Data Mining, pp. 793–802. ACM, New York (2010)Google Scholar
  13. 13.
    Luce, R., Perry, A.: A method of matrix analysis of group structure. Psychometrika 14(2), 95–116 (1949)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Milgram, S.: The Small World Problem. Psychology Today 2, 60–67 (1967)Google Scholar
  15. 15.
    Ranu, S., Singh, A.K.: Graphsig: A scalable approach to mining significant subgraphs in large graph databases. In: Proceedings of the 2009 IEEE International Conference on Data Engineering, pp. 844–855. IEEE Computer Society, Washington, DC, USA (2009)CrossRefGoogle Scholar
  16. 16.
    Saigo, H., Krämer, N., Tsuda, K.: Partial least squares regression for graph mining. In: Proceeding of the 14th ACM International Conference on Knowledge Discovery and Data Mining, pp. 578–586. ACM, New York (2008)Google Scholar
  17. 17.
    Seidman, S.B.: Network structure and minimum degre. Social Networks 5, 269–287 (1983)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Tao, Y., Papadias, D., Lian, X.: Reverse knn search in arbitrary dimensionality. In: Proceedings of the 30th International Conference on Very Large Data Bases, pp. 744–755. Very Large Data Bases Endowment (2004)Google Scholar
  19. 19.
    Thoma, M., Cheng, H., Gretton, A., Han, J., Peter Kriegel, H., Smola, A., Song, L., Yu, P.S., Yan, X., Borgwardt, K.: Near-optimal supervised feature selection among frequent subgraphs. In: SIAM Int’l Conf. on Data Mining (2009)Google Scholar
  20. 20.
    Thomason, B.E., Coffman, T.R., Marcus, S.E.: Sensitivity of social network analysis metrics to observation noise. In: IEEE Aerospace Conference, pp. 3206–3216 (2004)Google Scholar
  21. 21.
    University of Michigan: The origin of power-laws in internet topologies revisited. Web page,
  22. 22.
    Wang, H., He, H., Yang, J., Yu, P.S., Yu, J.X.: Dual labeling: Answering graph reachability queries in constant time. In: Proceedings of the 22nd International Conference on Data Engineering, p. 75. IEEE Computer Society, Washington, DC, USA (2006)Google Scholar
  23. 23.
    Yan, X., Cheng, H., Han, J., Yu, P.S.: Mining significant graph patterns by leap search. In: Proceedings of the 2008 ACM International Conference on Management of Data, pp. 433–444. ACM, New York (2008)Google Scholar
  24. 24.
    Zeng, Z., Tung, A.K.H., Wang, J., Feng, J., Zhou, L.: Comparing stars: on approximating graph edit distance. Proc. VLDB Endow. 2, 25–36 (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Linhong Zhu
    • 1
  • Wee Keong Ng
    • 2
  • Shuguo Han
    • 1
  1. 1.Institute for Infocomm ResearchSingapore
  2. 2.Nanyang Technological UniversitySingapore

Personalised recommendations