Modularity Based Hierarchical Community Detection in Networks

  • Vinícius da F. Vieira
  • Carolina R. Xavier
  • Nelson F. F. Ebecken
  • Alexandre G. Evsukoff
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8584)


The organization of nodes in communities, i.e., groups of nodes with many internal connections and few external connections, is one of the main structural features of networks and community detection is one of the most challenging tasks in networks. The communities in networks can be observed in different levels and a great number of methods can be found in the literature in order to identify the hierarchical organization of the communities. This work proposes a methodology for the representation of the hierarchical organization of communities in complex networks based on the spectral method of Newman. The proposed methodology, in contrast to other traditional approaches found in the literature, use the modularity, one of the most adopted measures for the quality of communities, in order to define the distances between the communities in the network. The methodology provides, as output, a dendrogram in order to illustrate the hierarchical organization of communities in networks. The application of the methodology to large scale networks show that the hierarchical visualization enhances the understanding of the complex systems modelled by networks, providing a broader view of the community structures.


Spectral Method Betweenness Centrality Community Detection Hierarchical Organization Collaboration Network 
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.
    Agarwal, G., Kempe, D.: Modularity-maximizing graph communities via mathematical programming. European Physical Journal B 66(3), 409–418 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Balay, S., Brown, J., Buschelman, K., Eijkhout, V., Gropp, W.D., Kaushik, D., Knepley, M.G., McInnes, L.C., Smith, B.F., Zhang, H.: PETSc users manual. Technical Report ANL-95/11 - Revision 3.3, Argonne National Laboratory (2012)Google Scholar
  3. 3.
    Vincent, D.: Blondel, Jean-Loup Guillaume, Renaud Lambiotte, and Etienne Lefebvre. Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment 2008(10) (2008)Google Scholar
  4. 4.
    Clauset, A., Newman, M.E.J., Moore, C.: Finding community structure in very large networks. Phys. Rev. E. 70(6), 066111 (2004)CrossRefGoogle Scholar
  5. 5.
    Clauset, A., Moore, C., Newman, M.E.J.: Hierarchical structure and the prediction of missing links in networks. Nature 453(7191), 98–101 (2008)CrossRefGoogle Scholar
  6. 6.
    Clauset, A., Moore, C., Newman, M.E.J.: Structural inference of hierarchies in networks. In: Airoldi, E.M., Blei, D.M., Fienberg, S.E., Goldenberg, A., Xing, E.P., Zheng, A.X. (eds.) ICML 2006. LNCS, vol. 4503, pp. 1–13. Springer, Heidelberg (2007)Google Scholar
  7. 7.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. The MIT Press (2001)Google Scholar
  8. 8.
    Danon, L., Diaz-Guilera, A., Arenas, A.: Effect of size heterogeneity on community identification in complex networks. Journal of Stat. Mech.: Theory and Experiment 2006(11), 6 (2006)CrossRefGoogle Scholar
  9. 9.
    Duch, J., Arenas, A.: Community detection in complex networks using extremal optimization. Physical Review E: Statistical, Nonlinear and Soft Matter Physics 72(2), 027104+ (2005)CrossRefGoogle Scholar
  10. 10.
    Fortunato, S.: Community detection in graphs. Physics Reports 486, 75–174 (2010)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Freeman, L.: Centrality in social networks: Conceptual clarification. Social Networks 1(3), 215–239 (1979)CrossRefGoogle Scholar
  12. 12.
    Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proceedings of the National Academy of Sciences 99(12), 7821–7826 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Girvan, M., Newman, M.E.J.: Community structure in social and biological networks (December 2001)Google Scholar
  14. 14.
    Guimerà, R., Amaral, L.: Functional cartography of complex metabolic networks. Nature 433, 895–900 (2005)CrossRefGoogle Scholar
  15. 15.
    Han, J., Kamber, M.: Data Mining: Concepts and Techniques, 1st edn. Morgan Kaufmann (2005)Google Scholar
  16. 16.
    Hastie, T., Tibshirani, R., Friedman, J.H.: The Elements of Statistical Learning. Springer (July 2003)Google Scholar
  17. 17.
    Kernighan, B.W., Lin, S.: An Efficient Heuristic Procedure for Partitioning Graphs. The Bell System Technical Journal 49(1), 291–307 (1970)CrossRefzbMATHGoogle Scholar
  18. 18.
    Cosentino, M., Lagomarsino, P., Jona, B.: Bassetti, and H. Isambert. Hierarchy and feedback in the evolution of the Escherichia coli transcription network. Proc. Natl. Acad. Sci. U S A 104(13), 5516–5520 (2007)CrossRefGoogle Scholar
  19. 19.
    Lancichinetti, A., Fortunato, S., Kertesz, J.: Detecting the overlapping and hierarchical community structure of complex networks. New Journal of Physics (February 2009)Google Scholar
  20. 20.
    Leon-Suematsu, Y.I., Yuta, K.: Framework for fast identification of community structures in large-scale social networks. In: Data Mining for Social Network Data. Annals of Information Systems, vol. 12, pp. 149–175. Springer US (2010)Google Scholar
  21. 21.
    Newman, M.E.J.: Modularity and community structure in networks. Proceedings of the National Academy of Sciences of the United States of America 103(23), 8577–8582 (2006)CrossRefGoogle Scholar
  22. 22.
    Newman, M.E.J.: Networks: An Introduction, 1st edn. Oxford University Press, USA (2010)CrossRefGoogle Scholar
  23. 23.
    Newman, M.E.J.: Communities, modules and large-scale structure in networks. Nature Physics 8(1), 25–31 (2012)CrossRefGoogle Scholar
  24. 24.
    Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Physical Review E: Statistical, Nonlinear and Soft Matter Physics 69(2) (February 2004)Google Scholar
  25. 25.
    Radicchi, F., Castellano, C., Cecconi, F., Loreto, V., Parisi, D.: Defining and identifying communities in networks. Proceedings of the National Academy of Sciences of the United States of America 101(9), 2658–2663 (2004)CrossRefGoogle Scholar
  26. 26.
    Ravasz, E., Somera, A.L., Mongru, D.A., Oltvai, Z.N., Barabasi, A.L.: Hierarchical organization of modularity in metabolic networks. Science 297(5586), 1551–1555 (2002)CrossRefGoogle Scholar
  27. 27.
    Sales-Pardo, M., Guimerà, R., Moreira, A.A., Amaral, L.A.N.: Extracting the hierarchical organization of complex systems. Proceedings of the National Academy of Sciences 104(39), 15224–15229 (2007)CrossRefGoogle Scholar
  28. 28.
    Vieira, V.F.: Detecção de Comunidades em Redes Complexas de Larga Escala. PhD thesis, Rio de Janeiro, RJ, Brazil (2013)Google Scholar
  29. 29.
    da Fonseca Vieira, V., Evsukoff, A.G.: A comparison of methods for community detection in large scale networks. In: Menezes, R., Evsukoff, A., González, M.C. (eds.) Complex Networks. SCI, vol. 424, pp. 75–86. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  30. 30.
    Wakita, K., Tsurumi, T.: Finding community structure in mega-scale social networks. Analysis 105(2), 9 (2007)Google Scholar
  31. 31.
    Zachary, W.W.: An information flow model for conflict and fission in small groups. J. Anthropol. Res. 33, 452–473 (1977)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Vinícius da F. Vieira
    • 1
    • 2
  • Carolina R. Xavier
    • 1
    • 2
  • Nelson F. F. Ebecken
    • 1
  • Alexandre G. Evsukoff
    • 1
    • 3
  1. 1.COPPE/UFRJ - Federal University of Rio de JaneiroRio de JaneiroBrazil
  2. 2.UFSJ - Federal University of São João del Rei, São João del Rei-MGBrazil
  3. 3.EMAp/FGV - Getślio Vargas FoundationRio de JaneiroBrazil

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