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Triadic analysis of affiliation networks



Triadic closure has been conceptualized and measured in a variety of ways, most famously the clustering coefficient. Existing extensions to affiliation networks, however, are sensitive to repeat group attendance, which does not reflect common interpersonal interpretations of triadic closure. This paper proposes a measure of triadic closure in affiliation networks designed to control for this factor, which manifests in bipartite models as biclique proliferation. To avoid arbitrariness, the paper introduces a triadic framework for affiliation networks, within which a range of measures can be defined; it then presents a set of basic axioms that suffice to narrow this range to the one measure. An instrumental assessment compares the proposed and two existing measures for reliability, validity, redundancy, and practicality. All three measures then take part in an investigation of three empirical social networks, which illustrates their differences.



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Admiraal, R., & Handcock, M. S. (2008). Networksis: A package to simulate bipartite graphs with fixed marginals through sequential importance sampling. Journal of Statistical Software, 24 (8), 121.
Altman, D. G., & Bland, J. M. (1983). Measurement in medicine: The analysis of method comparison studies. The Statistician, 32 (3), 307317.
Bonacich, P. (1991). Simultaneous group and individual centralities. Social Networks, 13 (2), 155168.
Bondy, J. A., & Murty, U. S. R. (2008). Graph theory, Graduate texts in mathematics. Berlin: Springer.
Borgatti, S. P., & Everett, M. G. (1997). Network analysis of 2-mode data. Social networks, 19, 243269.
Borgatti, S. P., & Halgin, D. S. (2011). Analyzing affiliation networks. In Scott, J., & Carrington, P. J. (Eds.), The sage handbook of social network analysis (pp. 417433). London: SAGE Publications Ltd.
Breiger, R. L. (1974). The duality of persons and groups. Social Forces, 53 (2), 181190.
Brunson, J. C., Fassino, S., McInnes, A., Narayan, M., Richardson, B., Franck, C., . . . Laubenbacher, R. C. (2014). Evolutionary events in a mathematical sciences research collaboration network . Scientometrics, 99 (3), 973998.
Burt, R. S. (1992). Structural holes: The social structure of competition. Cambridge, MA: Harvard University Press.
Carrino, C. N. (2006). A study of repeat collaboration in social affiliation networks. Ph.D. thesis, University Park, PA, USA. AAI3343661.
Chen, Y., Diaconis, P., Holmes, S. P., & Liu, J. S. (2005). Sequential Monte Carlo methods for statistical analysis of tables. Journal of the American Statistical Association, 100 (469), 109120.
Comin, C. H., Silva, F. N., & da F. Costa, L. (2015). A framework for evaluating complex networks measurements . EPL (Europhysics letters), 110 (6), 68002.
Csardi, G., & Nepusz, T. (2006). The igraph software package for complex network research. Interjournal, Complex Systems, 1695.
Davis, A., Gardner, B. B., & Gardner, M. R. (1941). Deep south; a social anthropological study of caste and class. Chicago: The University of Chicago Press.
Davis, J. A. (1967). Clustering and structural balance in graphs. Human Relations, 20 (2), 181187.
de Sola Pool, I., & Kochen, M. (1978). Contacts and influence. Socnet, 1 (1), 551.
Easley, D., & Kleinberg, J. (2010). Networks, crowds, and markets: Reasoning about a highly connected world. New York, USA: Cambridge University Press.
Faust, K. (1997). Centrality in affiliation networks. Social Networks, 19 (2), 157191.
Freeman, L. C. (1992). The sociological concept of “group”: An empirical test of two models. The American Journal of Sociology, 98 (1), 152166.
Freeman, L. C. (2003). Finding social groups: A meta-analysis of the southern women data. (pp. 3997). Breiger, Ronald, Carley, Kathleen, & Pattison, Philippa (eds), Dynamic social network modeling and analysis: Workshop summary and papers National Academics Press.
Galaskiewicz, J. (1985). Social organization of an urban grants economy: A study of business philanthropy and non-profit organizations. Orlando, FL: Academic Press.
Glänzel, W., & Schubert, A. (2004). Analyzing scientific networks through co-authorship. Open Access publications from Katholieke Universiteit Leuven. Katholieke Universiteit Leuven.
Granovetter, M. S. (1973). The strength of weak ties. The American Journal of Sociology, 78 (6), 13601380.
Gupte, M., & Eliassi-Rad, T. (2012). Measuring tie strength in implicit social networks. In Contractor, N. S., Uzzi, B., Macy, M. W., & Nejdl, W. (Eds.), Websci (pp. 109118). Proceedings of the 4th annual acm web science conference. WebSci '12. New York, NY, USA: ACM.
Harary, F., & Kommel, H. J. (1979). Matrix measures for transitivity and balance. Journal of Mathematical Sociology, 6 (2), 199210.
Hell, P. (1979). An introduction to the category of graphs. Topics in graph theory (New York, 1977) (pp. 120136) Ann. New York Acad. Sci., vol. 328. New York: Acad. Sci.
Holland, P. W., & Leinhardt, S. (1971). Transitivity in structural models of small groups. Small Group Research, 2 (2), 107124.
Kimberlin, C. L., & Winterstein, A. G. (2008). Validity and reliability of measurement instruments used in research. American Journal of Health-System Pharmacy, 65 (23), 22762284.
Kreher, D. L., & Stinson, D. R. (1999). Combinatorial algorithms: generation, enumeration, and search . SIGACT news, 30 (1), 3335.
Lee, C., & Cunningham, P. (2014). Community detection: Effective evaluation on large social networks. Journal of Complex Networks, 2 (1), 1937.
Liebig, J., & Rao, A. (2014). Identifying influential nodes in bipartite networks using the clustering coefficient. In Proceedings of the 10th International Conference on Signal-Image Technology and Internet-Based Systems.
Lind, P. G., González, M. C., & Herrmann, H. J. (2005). Cycles and clustering in bipartite networks. Physical Review E, 72 (Nov), 056127.
Martin, T., Ball, B., Karrer, B., & Newman, M. E. J. (2013). Coauthorship and citation patterns in the physical review. Physical Review E, 88 (Jul), 012814.
Mitchell, B. (1965). Theory of categories. Pure and Applied Mathematics, vol. 17. New York and London: Academic Press.
Newman, M. E. J. (2001). Scientific collaboration networks. I. Network construction and fundamental results. Physical Review E, 45 (2), 167256 (electronic).
Newman, M. E. J. (2003). The structure and function of complex networks. SIAM Review, 45 (2), 167256 (electronic).
Newman, M. E. J., Strogatz, S. H., & Watts, D. J. (2001). Random graphs with arbitrary degree distributions and their applications. Physical Review E, 64 (Jul), 026118.
Opsahl, T. (2013). Triadic closure in two-mode networks: Redefining the global and local clustering coefficients. Social Networks, 35 (2), 159167. Special Issue on Advances in Two-mode Social Networks.
R Development Core Team. (2008). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0.
Ravasz, E., Somera, A. L., Mongru, D. A., Oltvai, Z. N., & Barabási, A.-L. (2002). Hierarchical organization of modularity in metabolic networks. Science, 297 (5586), 1551.
Saramäki, J., Kivelä, M., Onnela, J.-P., Kaski, K., & Kertész, J. (2007). Generalizations of the clustering coefficient to weighted complex networks. Physical Review E, 75 (Feb), 027105.
Stanley, R. P. (2002). Enumerative combinatorics. Cambridge Studies in Advanced Mathematics, no. v. 1. Cambridge: Cambridge University Press.
Szabó, G., Alava, M., & Kertész, J. (2003). Structural transitions in scale-free networks. Physical Review E, 67 (5), 056102.
Uzzi, B., & Spiro, J. (2005). Collaboration and creativity: The small world problem. American Journal of Sociology, 111 (2), 447504.
Vázquez, A. (2003). Growing network with local rules: Preferential attachment, clustering hierarchy, and degree correlations. Physical Review E, 67 (May), 056104.
Wasserman, S., & Faust, K. (1994). Social network analysis: Methods and applications. vol. 8. Cambridge: Cambridge university press.
Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of “small-world” networks. Nature, 393 (6684), 440442.
Wickham, H. (2009). ggplot2: elegant graphics for data analysis. New York: Springer.


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