Network ensemble clustering using latent roles

  • Ulrik Brandes
  • Jürgen Lerner
  • Uwe NagelEmail author
Regular Article


We present a clustering method for collections of graphs based on the assumptions that graphs in the same cluster have a similar role structure and that the respective roles can be founded on implicit vertex types. Given a network ensemble (a collection of attributed graphs with some substantive commonality), we start by partitioning the set of all vertices based on attribute similarity. Projection of each graph onto the resulting vertex types yields feature vectors of equal dimensionality, irrespective of the original graph sizes. These feature vectors are then subjected to standard clustering methods. This approach is motivated by social network concepts, and we demonstrate its utility on an ensemble of personal networks of migrants, where we extract structurally similar groups and show their resemblance to predicted acculturation strategies.


Social network analysis Clustering Network ensembles Acculturation 

Mathematics Subject Classification (2000)

62H30 91D30 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Berry JW (1997) Immigration, acculturation, and adaptation. Appl Psychol 46(1): 5–68Google Scholar
  2. Boguñá M, Pastor-Satorras R, Díaz-Guilera A, Arenas A (2004) Models of social networks based on social distance attachment. Phys Rev E 70(056122)Google Scholar
  3. Brandes U, Lerner J, Lubbers MJ, McCarty C, Molina JL (2008) Visual statistics for collections of clustered graphs. In: Proceedings of the IEEE pacific visualization symposium (PacificVis’08). IEEE Computer Society, pp 47–54Google Scholar
  4. Brandes U, Lerner J, Nagel U, Nick B (2009) Structural trends in network ensembles. In: Complex networks, volume 207 of studies in computational intelligence. Springer, pp 83–97Google Scholar
  5. Brandes U, Lerner J, Lubbers MJ, McCarty C, Molina JL, Nagel U (2010) Recognizing modes of acculturation in personal networks of migrants. Procedia Soc Behav Sci 4:4–13 (Applications of Social Network Analysis)Google Scholar
  6. Bunke H, Allermann G (1983) Inexact graph matching for structural pattern recognition. Pattern Recogn Lett 1(4): 245–253zbMATHCrossRefGoogle Scholar
  7. Bunke H, Foggia P, Guidobaldi C, Vento M (2003) Graph clustering using the weighted minimum common supergraph. In: Graph based representations in pattern recognition, volume 2726 of LNCS. Springer, pp 235–246Google Scholar
  8. Butts CT, Carley KM (2005) Some simple algorithms for structural comparison. Comput Math Organ Theory 11(4): 291–305zbMATHCrossRefGoogle Scholar
  9. Deshpande M, Kuramochi M, Wale N, Karypis G (2005) Frequent substructure-based approaches for classifying chemical compounds. IEEE Trans Knowl Data Eng 17(8): 1036–1050CrossRefGoogle Scholar
  10. Faust K (2006) Comparing social networks: size, density, and local structure. Metodološki zvezki 3(2): 185–216Google Scholar
  11. Faust K, Skvoretz J (2002) Comparing networks across space and time, size and species. Soc Methodol 32(1): 267–299CrossRefGoogle Scholar
  12. Fortunato S (2010) Community detection in graphs. Phys Rep 486: 75–174MathSciNetCrossRefGoogle Scholar
  13. Fraley C, Raftery AE (2002) Model-based clustering, discriminant analysis and density estimation. J Am Stat Assoc 97(458): 611–631MathSciNetzbMATHCrossRefGoogle Scholar
  14. Gärtner T (2003) A survey of kernels for structured data. ACM SIGKDD Explor Newsl 5(1): 49–58CrossRefGoogle Scholar
  15. Gärtner T, Flach P, Wrobel S (2003) On graph kernels: hardness results and efficient alternatives. In: Proceedings of the 16th annual conference on computational learning theory and 7th kernel workshop, volume 2777 of LNCS. Springer, pp 29–143Google Scholar
  16. Heil GH, White HC (1976) An algorithm for finding simultaneous homomorphic correspondences between graphs and their image graphs. Behav Sci 21(1): 26–35CrossRefGoogle Scholar
  17. Hlaoui A, Wang S (2003) A new median graph algorithm. In: Graph based representations in pattern recognition, volume 2726 of LNCS. Springer, pp 225–234Google Scholar
  18. Hlaoui A, Wang S (2006) Median graph computation for graph clustering. Soft Comput Fusion Found Methodol Appl 10(1): 47–53Google Scholar
  19. Holland PW, Laskey KB, Leinhardt S (1983) Stochastic blockmodels: first steps. Soc Netw 5(2): 109–137MathSciNetCrossRefGoogle Scholar
  20. Horváth T (2005) Cyclic pattern kernels revisited. In: Advances in knowledge discovery and data mining, volume 3518 of LNAI. Springer, pp 791–801Google Scholar
  21. Horváth T, Gärtner T, Wrobel S (2004) Cyclic pattern kernels for predictive graph mining. In: KDD ’04: proceedings of the tenth ACM SIGKDD international conference on knowledge discovery and data mining. ACM, pp 158–167Google Scholar
  22. Jain BJ, Wysotzki F (2004) Central clustering of attributed graphs. Mach Learn 56(1–3): 169–207zbMATHCrossRefGoogle Scholar
  23. Jain BJ, Geibel P, Wysotzki F (2005) SVM learning with the Schur-Hadamard inner product for graphs. Neurocomputing 64: 93–105CrossRefGoogle Scholar
  24. Jiang X, Münger A, Bunke H (1999) Computing the generalized median of a set of graphs. In: Proceedings of the 2nd IAPR workshop on graph-based representations, pp 115–124Google Scholar
  25. Jiang X, Münger A, Bunke H (2001) On median graphs: properties, algorithms, and applications. IEEE Trans Pattern Anal Mach Intell 23(10): 1144–1151CrossRefGoogle Scholar
  26. Kalish Y, Robins G (2006) Psychological predispositions and network structure: the relationship between individual predispositions, structural holes and network closure. Soc Netw 28(1): 56–84CrossRefGoogle Scholar
  27. Lerner J (2005) Role assignments. In: Brandes U, Erlebach T (eds) Network analysis. Springer, Berlin, pp 216–252CrossRefGoogle Scholar
  28. Luo B, Robles-Kelly A, Torsello A, Wilson RC, Hancock ER (2001) A probabilistic framework for graph clustering. In: IEEE computer society conference on computer vision and pattern recognition (CVPR’01), vol 1. IEEE computer society, pp 912–919Google Scholar
  29. Luo B, Wilson RC, Hancock ER (2002) Spectral feature vectors for graph clustering. In: Structural, syntactic, and statistical pattern recognition, volume 2396 of LNCS. Springer, pp 423–454Google Scholar
  30. Luo B, Wilson RC, Hancock ER (2003) Spectral feature vectors for graph clustering. In: Graph based representations in pattern recognition, volume 2726 of LNCS. Springer, pp 190–201Google Scholar
  31. McSherry F (2001) Spectral partitioning of random graphs. In: Proceedings of the 42nd annual IEEE symposium on foundations of computer science (FOCS’01). IEEE Computer Society, pp 529–537Google Scholar
  32. Molina JL, Lerner J, Mestres SG (2008) Patrones de cambio de las redes personales de inmigrantes en Cataluña. Redes 15: 50–63Google Scholar
  33. Münger A, Bunke H, Jiang X (1999) Combinatorial search vs. genetic algorithms: a case study based on the generalized median graph problem. Pattern Recogn Lett 20(11–13): 1271–1279Google Scholar
  34. Nadel SF (1957) The theory of social structure. Cohen & West. Reprinted by Routledge, 2004Google Scholar
  35. Neuhaus M, Bunke H (2006) A random walk kernel derived from graph edit distance. In: Structural, syntactic, and statistical pattern recognition, volume 4109 of LNCS. Springer, pp 191–199Google Scholar
  36. Schaeffer SE (2007) Graph clustering. Comput Sci Rev 1(1): 27–64MathSciNetCrossRefGoogle Scholar
  37. Serratosa F (2000) Function-described graphs for structural pattern recognition. PhD thesis, Institut d’Organització i Control de Sistemes IndustrialsGoogle Scholar
  38. Welser HT, Gleave E, Fisher D, Smith M (2007) Visualizing the signatures of social roles in online discussion groups. J Soc Struct 8Google Scholar
  39. Wong A, You M (1985) Entropy and distance of random graphs with application to structural pattern recognition. IEEE Trans Pattern Anal Mach Intell 7: 599–609zbMATHCrossRefGoogle Scholar
  40. Wong A, Constant J, You M (1990) Random graphs. In: Bunke H, Sanfeliu A (eds) Syntactic and structural pattern recognition: theory and applications. World Scientific, pp 197–234Google Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Computer and Information ScienceUniversity of KonstanzKonstanzGermany

Personalised recommendations