Edge Role Discovery via Higher-Order Structures

  • Nesreen K. Ahmed
  • Ryan A. Rossi
  • Theodore L. Willke
  • Rong Zhou
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10234)


Previous work in network analysis has focused on modeling the roles of nodes in graphs. In this paper, we introduce edge role discovery and propose a framework for learning and extracting edge roles from large graphs. We also propose a general class of higher-order role models that leverage network motifs. This leads us to develop a novel edge feature learning approach for role discovery that begins with higher-order network motifs and automatically learns deeper edge features. All techniques are parallelized and shown to scale well. They are also efficient with a time complexity of \(\mathcal {O}(|E|)\). The experiments demonstrate the effectiveness of our model for a variety of ML tasks such as improving classification and dynamic network analysis.


Role discovery Edge roles Higher-order network analysis Graphlets Network motifs Latent space models Transfer learning 


  1. 1.
    Ahmed, N.K., Neville, J., Rossi, R.A., Duffield, N.: Efficient graphlet counting for large networks. In: ICDM, p. 10 (2015)Google Scholar
  2. 2.
    Ahmed, N.K., Neville, J., Rossi, R.A., Duffield, N., Willke, T.L.: Graphlet decomposition: framework, algorithms, and applications. KAIS 50(3), 1–32 (2016)Google Scholar
  3. 3.
    Ahmed, N.K., Willke, T.L., Rossi, R.A.: Estimation of local subgraph counts. In: IEEE BigData, pp. 1–10 (2016)Google Scholar
  4. 4.
    Akaike, H.: A new look at the statistical model identification. TOAC 19(6), 716–723 (1974)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Anderson, C., Wasserman, S., Faust, K.: Building stochastic blockmodels. Soc. Netw. 14(1), 137–161 (1992)CrossRefGoogle Scholar
  6. 6.
    Arabie, P., Boorman, S., Levitt, P.: Constructing blockmodels: how and why. J. Math. Psychol. 17(1), 21–63 (1978)CrossRefzbMATHGoogle Scholar
  7. 7.
    Batagelj, V., Mrvar, A., Ferligoj, A., Doreian, P.: Generalized blockmodeling with pajek. Metodoloski Zvezki 1, 455–467 (2004)Google Scholar
  8. 8.
    Bennett, W.R.: Spectra of quantized signals. Bell Syst. Tech. 27(3), 446–472 (1948)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Borgatti, S., Everett, M., Johnson, J.: Analyzing Social Networks. SAGE Publications, Thousand Oaks (2013)Google Scholar
  10. 10.
    Bregman, L.M.: The relaxation method of finding the common point of convex sets. USSR Comput. Math. Math. Phys. 7(3), 200–217 (1967)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Doreian, P., Batagelj, V., Ferligoj, A.: Generalized Blockmodeling, vol. 25. Cambridge University Press, Cambridge (2005)zbMATHGoogle Scholar
  12. 12.
    Getoor, L., Taskar, B. (eds.): Introduction to Statistical Relational Learning. MIT Press, Cambridge (2007)zbMATHGoogle Scholar
  13. 13.
    Grünwald, P.D.: The Minimum Description Length Principle. MIT Press, Cambridge (2007)Google Scholar
  14. 14.
    Henderson, K., et al.: Rolx: structural role extraction & mining in large graphs. In: KDD, pp. 1231–1239 (2012)Google Scholar
  15. 15.
    Holland, P.W., Laskey, K.B., Leinhardt, S.: Stochastic blockmodels: first steps. Soc. Netw. 5(2), 109–137 (1983)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Huffman, D.A., et al.: A method for the construction of minimum-redundancy codes. Proc. IRE 40(9), 1098–1101 (1952)CrossRefzbMATHGoogle Scholar
  17. 17.
    Li, M., Vitányi, P.: An Introduction to Kolmogorov Complexity and Its Applications. Springer Science & Business Media, Heidelberg (2009)zbMATHGoogle Scholar
  18. 18.
    Lloyd, S.: Least squares quantization in PCM. TOIT 28(2), 129–137 (1982)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Lorrain, F., White, H.: Structural equivalence of individuals in social networks. J. Math. Sociol. 1(1), 49–80 (1971)CrossRefGoogle Scholar
  20. 20.
    Macskassy, S., Provost, F.: A simple relational classifier. In: KDD MRDM (2003)Google Scholar
  21. 21.
    Macskassy, S.A., Provost, F.: Classification in networked data: a toolkit and a univariate case study. JMLR 8, 935–983 (2007)Google Scholar
  22. 22.
    Max, J.: Quantizing for minimum distortion. TOIT 6(1), 7–12 (1960)MathSciNetGoogle Scholar
  23. 23.
    Nowicki, K., Snijders, T.: Estimation and prediction for stochastic blockstructures. J. Am. Stat. Assoc. 96(455), 1077–1087 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Oliver, B., Pierce, J., Shannon, C.E.: The philosophy of PCM. IRE 36(11), 1324–1331 (1948)CrossRefGoogle Scholar
  25. 25.
    Rahman, M., Hasan, M.A.: Link prediction in dynamic networks using graphlet. In: Frasconi, P., Landwehr, N., Manco, G., Vreeken, J. (eds.) ECML PKDD 2016. LNCS (LNAI), vol. 9851, pp. 394–409. Springer, Cham (2016). doi: 10.1007/978-3-319-46128-1_25 CrossRefGoogle Scholar
  26. 26.
    Rissanen, J.: Modeling by shortest data description. Automatica 14(5), 465–471 (1978)CrossRefzbMATHGoogle Scholar
  27. 27.
    Rossi, R.A., Ahmed, N.K.: The network data repository with interactive graph analytics and visualization. In: AAAI (2015).
  28. 28.
    Rossi, R.A., Ahmed, N.K.: Role discovery in networks. TKDE 27(4), 1112 (2015)Google Scholar
  29. 29.
    Rossi, R.A., Gallagher, B., Neville, J., Henderson, K.: Role-dynamics: fast mining of large dynamic networks. In: WWW Companion, pp. 997–1006 (2012)Google Scholar
  30. 30.
    Rossi, R.A., Gallagher, B., Neville, J., Henderson, K.: Modeling dynamic behavior in large evolving graphs. In: WSDM, pp. 667–676 (2013)Google Scholar
  31. 31.
    Rossi, R.A., McDowell, L.K., Aha, D.W., Neville, J.: Transforming graph data for statistical relational learning. JAIR 45(1), 363–441 (2012)zbMATHGoogle Scholar
  32. 32.
    Rossi, R.A., Zhou, R.: Parallel collective factorization for modeling large heterogeneous networks. Soc. Netw. Anal. Mining 6(1), 30 (2016)CrossRefGoogle Scholar
  33. 33.
    Schwarz, G., et al.: Estimating the dimension of a model. Ann. Stat. 6(2), 461–464 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. 27(1), 379–423 (1948)MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Van Leeuwen, J.: On the construction of Huffman trees. In: ICALP, p. 382 (1976)Google Scholar
  36. 36.
    Vishwanathan, S.V.N., Schraudolph, N.N., Kondor, R., Borgwardt, K.M.: Graph kernels. JMLR 11, 1201–1242 (2010)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Nesreen K. Ahmed
    • 1
  • Ryan A. Rossi
    • 2
  • Theodore L. Willke
    • 1
  • Rong Zhou
    • 2
  1. 1.Intel LabsSanta ClaraUSA
  2. 2.Palo Alto Research Center (Xerox PARC)Palo AltoUSA

Personalised recommendations