Skip to main content

Modularity Based Hierarchical Community Detection in Networks

  • Conference paper
Computational Science and Its Applications – ICCSA 2014 (ICCSA 2014)

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Agarwal, G., Kempe, D.: Modularity-maximizing graph communities via mathematical programming. European Physical Journal B 66(3), 409–418 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  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. 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. Clauset, A., Newman, M.E.J., Moore, C.: Finding community structure in very large networks. Phys. Rev. E. 70(6), 066111 (2004)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. The MIT Press (2001)

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  10. Fortunato, S.: Community detection in graphs. Physics Reports 486, 75–174 (2010)

    Article  MathSciNet  Google Scholar 

  11. Freeman, L.: Centrality in social networks: Conceptual clarification. Social Networks 1(3), 215–239 (1979)

    Article  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  13. Girvan, M., Newman, M.E.J.: Community structure in social and biological networks (December 2001)

    Google Scholar 

  14. Guimerà, R., Amaral, L.: Functional cartography of complex metabolic networks. Nature 433, 895–900 (2005)

    Article  Google Scholar 

  15. Han, J., Kamber, M.: Data Mining: Concepts and Techniques, 1st edn. Morgan Kaufmann (2005)

    Google Scholar 

  16. Hastie, T., Tibshirani, R., Friedman, J.H.: The Elements of Statistical Learning. Springer (July 2003)

    Google Scholar 

  17. Kernighan, B.W., Lin, S.: An Efficient Heuristic Procedure for Partitioning Graphs. The Bell System Technical Journal 49(1), 291–307 (1970)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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. 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)

    Article  Google Scholar 

  22. Newman, M.E.J.: Networks: An Introduction, 1st edn. Oxford University Press, USA (2010)

    Book  Google Scholar 

  23. Newman, M.E.J.: Communities, modules and large-scale structure in networks. Nature Physics 8(1), 25–31 (2012)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  28. Vieira, V.F.: Detecção de Comunidades em Redes Complexas de Larga Escala. PhD thesis, Rio de Janeiro, RJ, Brazil (2013)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  30. Wakita, K., Tsurumi, T.: Finding community structure in mega-scale social networks. Analysis 105(2), 9 (2007)

    Google Scholar 

  31. Zachary, W.W.: An information flow model for conflict and fission in small groups. J. Anthropol. Res. 33, 452–473 (1977)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

da F. Vieira, V., Xavier, C.R., Ebecken, N.F.F., Evsukoff, A.G. (2014). Modularity Based Hierarchical Community Detection in Networks. In: Murgante, B., et al. Computational Science and Its Applications – ICCSA 2014. ICCSA 2014. Lecture Notes in Computer Science, vol 8584. Springer, Cham. https://doi.org/10.1007/978-3-319-09153-2_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-09153-2_11

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09152-5

  • Online ISBN: 978-3-319-09153-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics