Abstract
Fuzzy community detection in social networks has caught researchers’ attention because, in most real world networks, the vertices (i.e., people) do not belong to only one community. Our recent work on generalized modularity motivated us to introduce a generalized fuzzy t-norm formulation of fuzzy modularity. We investigated four fuzzy t-norm operators, Product, Drastic, Lukasiewicz and Minimum, and the generalized Yager operator, with five well-known social network data sets. The experiments show that the Yager operator with a proper parameter value performs better than the product operator in revealing community structure: (1) the Yager operator can provide a more certain visualization of the number of communities for simple networks; (2) it can find a relatively small-sized community in a flat network; (3) it can detect communities in networks with hierarchical structures; and (4) it can uncover several reasonable covers in a complicated network. These findings lead us to believe that the Yager operator can play a big role in fuzzy community detection. Our future work is to build a theoretical relation between the Yager operator and different types of networks.
Keywords
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proceedings of the National Academy of Sciences of the United States of America, 7821–7826 (2002)
Havens, T.C., Bezdek, J.C., Leckie, C., Ramamohanarao, K., Palaniswami, M.: A soft modularity function for detecting fuzzy communities in social network (2012)
Yager, R.R.: On the general class of fuzzy connectives. Fuzzy Sets and Systems 4, 235–242 (1980)
Fortunato, S.: Community detection in graphs. Physics Reports, vol. 486, pp. 75–174 (2010)
Palla, G., Dernyi, I., Farkas, I., Vicsek, T.: Uncovering the overlapping community structure of complex networks in nature and society. Nature 435, 814–818 (2005)
Zhang, S., Wang, R., Zhang, X.: Identification of overlapping community structure in complex networks using fuzzy c-means clustering. Physics A: Statistical Mechanics and its Applications 374, 483–490 (2007)
Liu, J.: Fuzzy modularity and fuzzy community structure in networks. The European Physical Journal B 77(4), 547–557 (2010)
Zachary, W.W.: An information flow model for conflict and fission in small groups. Journal of Anthropological Research 33, 452–473 (1977)
Bezdek, J.C., Keller, J., Krisnapuram, R., Pal, N.: Fuzzy Models and Algorithms for Pattern Recognition and Image Processing. Kluwer Academic Publishers, Norwell (1999)
Zadeh, L.A.: Fuzzy sets. Information and Control 8(3), 338–353 (1965)
Michael, J.H., Massey, J.G.: Modeling the communication network in a sawmill. Forest Products 47, 25–30 (1997)
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. Behavioral Ecology and Sociobiology 54, 396–405 (2003)
Krebs, V.: Books about U.S.A. politics, http://www.orgnet.com/
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Su, J., Havens, T.C. (2014). A Generalized Fuzzy T-norm Formulation of Fuzzy Modularity for Community Detection in Social Networks. In: Jamshidi, M., Kreinovich, V., Kacprzyk, J. (eds) Advance Trends in Soft Computing. Studies in Fuzziness and Soft Computing, vol 312. Springer, Cham. https://doi.org/10.1007/978-3-319-03674-8_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-03674-8_7
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03673-1
Online ISBN: 978-3-319-03674-8
eBook Packages: EngineeringEngineering (R0)