Abstract
Empirical studies indicate that communities in real world networks are simultaneously overlapped and hierarchical. This implies that one node can participate in more than one community simultaneously and community further contains sub-communities. However, few methods are capable of simultaneously detecting the overlapping and hierarchical community structure in networks. In this chapter, taking maximal cliques as building blocks of community, a metric is proposed to quantify the overlapping community. With this metric, the overlapping community structure can be efficiently detected by directly finding the optimal partition of network using standard modularity. We also describe the applications on word association network and scientific collaboration network.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
CFinder is a free software for finding overlapping dense groups of nodes in networks, based on the clique percolation method. URL: www.cfinder.org.
References
Strogatz, S.H.: Exploring complex networks. Nature 410, 268–276 (2001)
Albert, R., Barabási, A.L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)
Newman, M.E.J.: The structure and function of complex networks. SIAM Rev. 45, 167–256 (2003)
Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. USA 99, 7821–7826 (2002)
Guimerà, R., Amaral, L.A.N.: Functional cartography of complex metabolic networks. Nature 433, 895–900 (2005)
Flake, G.W., Lawrence, S.R., Giles, C.L., Coetzee, F.M.: Self-organization and identification of Web communities. IEEE Comput. 35, 66–71 (2002)
Newman, M.E.J.: Finding community structure in networks using the eigenvectors of matrices. Phys. Rev. E 74, 036104 (2006)
Palla, G., Derényi, I., Farkas, I., Vicsek, T.: Uncovering the overlapping community structure of complex networks in nature and society. Nature 435, 814–818 (2005)
Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69, 026113 (2004)
Radicchi, F., Castellano, C., Cecconi, F., Loreto, V., Parisi, D.: Defining and identifying communities in networks. Proc. Natl. Acad. Sci. USA 101, 2658–2663 (2004)
Newman, M.E.J.: Fast algorithm for detecting community structure in networks. Phys. Rev. E 69, 066133 (2004)
Newman, M.E.J.: Modularity and community structure in networks. Proc. Natl. Acad. Sci. USA 103, 8577–8582 (2006)
Raghavan, U.N., Albert, R., Kumara, S.: Near linear time algorithm to detect community structures in large-scale networks. Phys. Rev. E 76, 036106 (2007)
Danon, L., Duch, J., Diaz-Guilera, A., Arenas, A.: Comparing community structure identification. J. Stat. Mech. P09008 (2005)
Clauset, A., Newman, M.E.J., Moore, C.: Finding community structure in very large networks. Phys. Rev. E 70, 066111 (2004)
Duch, J., Arenas, A.: Community detection in complex networks using extremal optimization. Phys. Rev. E 72, 027104 (2005)
Fortunato, S., Barthélemy, M.: Resolution limit in community detection. Proc. Natl. Acad. Sci. USA 104, 36–41 (2007)
Kumpula, J.M., Saramaki, J., Kaski, K., Kertesz, J.: Resolution limit in complex network community detection with Potts model approach. Eur. Phys. J. B 56, 41–45 (2007)
Baumes, J., Krishnamoorthy, M., Magdon-Ismail, M., Preston, N.: Finding communities by clustering a graph into overlapping subgraphs. In: Proceedings of IADIS International Conference Applied Computing, pp. 97–104 (2005)
Saito, K., Yamada, T., Kazama, K.: Extracting communities from complex networks by the k-dense method. In: Proceedings of the 6th IEEE International Conference on Data Mining, pp. 300–304 (2008)
Zhang, S., Wang, R.S., Zhang, X.S.: Identification of overlapping community structure in complex networks using fuzzy c-means clustering. Physica A 374, 483–490 (2007)
Palla, G., Farkas, I.J., Pollner, P., Derényi, I., Vicsek, T.: Directed network modules. New J. Phys. 9, 186 (2007)
Farkas, I.J., Ábel, D., Palla, G., Vicsek, T.: Weighted network modules. New J. Phys. 9, 180 (2007)
Nicosia, V., Mangioni, G., Carchiolo, V., Malgeri, M.: Extending modularity definition for directed graphs with overlapping communities. J. Stat. Mech. P03024 (2009)
Evans, T.S., Lambiotte, R.: Line graphs, link partitions, and overlapping communities. Phys. Rev. E 80, 016105 (2009)
Lancichinetti, A., Fortunato, S., Kertesz, J.: Detecting the overlapping and hierarchical community structure of complex networks. New J. Phys. 11, 033015 (2009)
Sales-Pardo, M., Guimerà, R., Moreira, A.A., Amaral, L.A.N.: Extracting the hierarchical organization of complex systems. Proc. Natl. Acad. Sci. USA 104, 15224–15229 (2007)
Ravasz, E., Somera, A.L., Mongru, D.A., Oltvai, Z.N., Barabási, A.L.: Hierarchical organization of modularity in metabolic networks. Science 297, 1551–1555 (2002)
Pons, P., Latapy, M.: Post-processing hierarchical community structures: Quality improvements and multi-scale view. Theoret. Comput. Sci. 412, 892–900 (2011)
Shen, H.W., Cheng, X.Q., Cai, K., Hu, M.B.: Detect overlapping and hierarchical community structure in networks. Physica A 388, 1706–1712 (2009)
Bron, C., Kerbosch, J.: Finding all cliques in an undirected graph. Commun. ACM 575–577 (1973)
Adamcsek, B., Palla, G., Farkas, I.J., Derényi, I., Vicsek, T.: CFinder: Locating cliques and overlapping modules in biological networks. Bioinformatics 22, 1021–1023 (2006)
Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)
Blondel, V.D., Guillaume, J.L., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. J. Stat. Mech. P10008 (2008)
Shen, H.W., Cheng, X.Q., Guo, J.F.: Quantifying and identifying the overlapping community structure in networks. J. Stat. Mech. P07042 (2009)
Arenas, A., Fernández, A., Gómez, S.: Analysis of the structure of complex networks at different resolution levels. New J. Phys. 10, 053039 (2008)
Lancichinetti, A., Fortunato, S.: Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities. Phys. Rev. E 80, 016118 (2009)
Zachary, W.W.: An information flow model for conflict and fission in small groups. J. Anthropol. Res. 33, 452–473 (1977)
Lusseau, D., Schneider, K., Boisseau, O.J., Haase, P., Slooten, E., Dawson, S.M.: The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations. Can geographic isolation explain this unique trait? Behav. Ecol. Sociobiol. 54, 396–405 (2003)
Nelson, D.L., McEvoy, C.L., Schreiber, T.A.: The University of South Florida word association, rhyme, and word fragment norms (1998). http://www.usf.edu/FreeAssociation/
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Shen, HW. (2013). Detecting the Overlapping and Hierarchical Community Structure in Networks. In: Community Structure of Complex Networks. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31821-4_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-31821-4_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31820-7
Online ISBN: 978-3-642-31821-4
eBook Packages: Computer ScienceComputer Science (R0)