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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Agarwal, G., Kempe, D.: Modularity-maximizing graph communities via mathematical programming. European Physical Journal B 66(3), 409–418 (2008)
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)
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)
Clauset, A., Newman, M.E.J., Moore, C.: Finding community structure in very large networks. Phys. Rev. E. 70(6), 066111 (2004)
Clauset, A., Moore, C., Newman, M.E.J.: Hierarchical structure and the prediction of missing links in networks. Nature 453(7191), 98–101 (2008)
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)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. The MIT Press (2001)
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)
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)
Fortunato, S.: Community detection in graphs. Physics Reports 486, 75–174 (2010)
Freeman, L.: Centrality in social networks: Conceptual clarification. Social Networks 1(3), 215–239 (1979)
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)
Girvan, M., Newman, M.E.J.: Community structure in social and biological networks (December 2001)
Guimerà, R., Amaral, L.: Functional cartography of complex metabolic networks. Nature 433, 895–900 (2005)
Han, J., Kamber, M.: Data Mining: Concepts and Techniques, 1st edn. Morgan Kaufmann (2005)
Hastie, T., Tibshirani, R., Friedman, J.H.: The Elements of Statistical Learning. Springer (July 2003)
Kernighan, B.W., Lin, S.: An Efficient Heuristic Procedure for Partitioning Graphs. The Bell System Technical Journal 49(1), 291–307 (1970)
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)
Lancichinetti, A., Fortunato, S., Kertesz, J.: Detecting the overlapping and hierarchical community structure of complex networks. New Journal of Physics (February 2009)
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)
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)
Newman, M.E.J.: Networks: An Introduction, 1st edn. Oxford University Press, USA (2010)
Newman, M.E.J.: Communities, modules and large-scale structure in networks. Nature Physics 8(1), 25–31 (2012)
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)
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)
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)
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)
Vieira, V.F.: Detecção de Comunidades em Redes Complexas de Larga Escala. PhD thesis, Rio de Janeiro, RJ, Brazil (2013)
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)
Wakita, K., Tsurumi, T.: Finding community structure in mega-scale social networks. Analysis 105(2), 9 (2007)
Zachary, W.W.: An information flow model for conflict and fission in small groups. J. Anthropol. Res. 33, 452–473 (1977)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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)