A Comparison of Agglomerative Hierarchical Algorithms for Modularity Clustering

  • Michael Ovelgönne
  • Andreas Geyer-SchulzEmail author
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


Modularity is a popular measure for the quality of a cluster partition. Primarily, its popularity originates from its suitability for community identification through maximization. A lot of algorithms to maximize modularity have been proposed in recent years. Especially agglomerative hierarchical algorithms showed to be fast and find clusterings with high modularity. In this paper we present several of these heuristics, discuss their problems and point out why some algorithms perform better than others. In particular, we analyze the influence of search heuristics on the balancedness of the merge process and show why the uneven contraction of a graph due to an unbalanced merge process leads to clusterings with comparable low modularity.


Modularity Maximization Cluster Partition Divisive Algorithm Cluster Pair Singleton Cluster 
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.



The research leading to these results has received funding from the European Community’s Seventh Framework Programme FP7/2007-2013 under grant agreement n ∘ 215453 - WeKnowIt.


  1. Agarwal G, Kempe D (2008) Modularity-maximizing graph communities via mathematical programming. Eur J Phys B 66:409–418MathSciNetzbMATHCrossRefGoogle 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(5):056,122Google Scholar
  3. Brandes U, Delling D, Gaertler M, Görke R, Hoefer M, Nikoloski Z, Wagner D (2008) On modularity clustering. IEEE Trans Knowl Data Eng 20(2):172–188CrossRefGoogle Scholar
  4. Clauset A, Newman MEJ, Moore C (2004) Finding community structure in very large networks. Phys Rev E 70Google Scholar
  5. Duch J, Arenas A (2005) Community detection in complex networks using extremal optimization. Phys Rev E 72(2):027,104Google Scholar
  6. Girvan M, Newman MEJ (2002) Community structure in social and biological networks. Proc Natl Acad Sci USA 99(12):7821–7826MathSciNetzbMATHCrossRefGoogle Scholar
  7. Kernighan B, Lin S (1970) An efficient heuristic procedure for partitioning graphs. Bell Syst Technical J 49(1):291–307zbMATHGoogle Scholar
  8. Lehmann S, Hansen L (2007) Deterministic modularity optimization. Eur Phys J B 60(1):83–88CrossRefGoogle Scholar
  9. Lü Z, Huang W (2009) Iterated tabu search for identifying community structure in complex networks. Phys Rev E 80(2):026,130Google Scholar
  10. Medus A, Acuña G, Dorso C (2005) Detection of community structures in networks via global optimization. Phys A 358(2-4):593–604Google Scholar
  11. Newman MEJ (2004) Fast algorithm for detecting community structure in networks. Phys Rev E 69Google Scholar
  12. Newman MEJ (2006) Modularity and community structure in networks. Proc Natl Acad Sci USA 103(23):8577–8582CrossRefGoogle Scholar
  13. Newman MEJ, Girvan M (2004) Finding and evaluating community structure in networks. Phys Rev E 69(2):026,113Google Scholar
  14. Ovelgönne M, Geyer-Schulz A (2010) Cluster cores and modularity maximization. In: ICDMW ’10. IEEE International Conference on Data Mining Workshops, pp 1204–1213Google Scholar
  15. Raghavan UN, Albert R, Kumara S (2007) Near linear time algorithm to detect community structures in large-scale networks. Phys Rev E 76(3):036,106Google Scholar
  16. Ruan J, Zhang W (2007) An efficient spectral algorithm for network community discovery and its applications to biological and social networks. In: Seventh IEEE International Conference on Data Mining, 2007, pp 643–648CrossRefGoogle Scholar
  17. Schuetz P, Caflisch A (2008) Efficient modularity optimization by multistep greedy algorithm and vertex mover refinement. Phys Rev E 77Google Scholar
  18. Wakita K, Tsurumi T (2007) Finding community structure in mega-scale social networks. CoRR abs/cs/0702048,
  19. White S, Smyth P (2005) A spectral clustering approach to finding communities in graphs. In: Proceedings of the Fifth SIAM International Conference on Data Mining, SIAM, pp 274–285Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Information Services and Electronic Markets, IISMKarlsruhe Institute of TechnologyKarlsruheGermany

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