Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-23T03:12:41.580Z Has data issue: false hasContentIssue false
  • English
  • Français

Triadic analysis of affiliation networks

Published online by Cambridge University Press:  22 December 2015

JASON CORY BRUNSON
JASON CORY BRUNSON*
Affiliation:
Center for Quantitative Medicine, UConn Health, Farmington, CT 06030, USA (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Keywords

affiliation networkstriadic closuretriad censusclustering coefficientbicliques
Type
Research Article
Information
Network Science , Volume 3 , Issue 4 , December 2015 , pp. 480 - 508
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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), 1–21.Google Scholar
Altman, D. G., & Bland, J. M. (1983). Measurement in medicine: The analysis of method comparison studies. The Statistician, 32 (3), 307–317.Google Scholar
Bonacich, P. (1991). Simultaneous group and individual centralities. Social Networks, 13 (2), 155–168.Google Scholar
Bondy, J. A., & Murty, U. S. R. (2008). Graph theory, Graduate texts in mathematics. Berlin: Springer.CrossRefGoogle Scholar
Borgatti, S. P., & Everett, M. G. (1997). Network analysis of 2-mode data. Social networks, 19, 243–269.Google Scholar
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. 417–433). London: SAGE Publications Ltd.Google Scholar
Breiger, R. L. (1974). The duality of persons and groups. Social Forces, 53 (2), 181–190.CrossRefGoogle Scholar
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), 973–998.Google Scholar
Burt, R. S. (1992). Structural holes: The social structure of competition. Cambridge, MA: Harvard University Press.Google Scholar
Carrino, C. N. (2006). A study of repeat collaboration in social affiliation networks. Ph.D. thesis, University Park, PA, USA. AAI3343661.Google Scholar
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), 109–120.Google Scholar
Comin, C. H., Silva, F. N., & da F. Costa, L. (2015). A framework for evaluating complex networks measurements . EPL (Europhysics letters), 110 (6), 68002.Google Scholar
Csardi, G., & Nepusz, T. (2006). The igraph software package for complex network research. Interjournal, Complex Systems, 1695.Google Scholar
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.Google Scholar
Davis, J. A. (1967). Clustering and structural balance in graphs. Human Relations, 20 (2), 181–187.Google Scholar
de Sola Pool, I., & Kochen, M. (1978). Contacts and influence. Socnet, 1 (1), 5–51.Google Scholar
Easley, D., & Kleinberg, J. (2010). Networks, crowds, and markets: Reasoning about a highly connected world. New York, USA: Cambridge University Press.CrossRefGoogle Scholar
Faust, K. (1997). Centrality in affiliation networks. Social Networks, 19 (2), 157–191.CrossRefGoogle Scholar
Freeman, L. C. (1992). The sociological concept of “group”: An empirical test of two models. The American Journal of Sociology, 98 (1), 152–166.Google Scholar
Freeman, L. C. (2003). Finding social groups: A meta-analysis of the southern women data. (pp. 39–97). Breiger, Ronald, Carley, Kathleen, & Pattison, Philippa (eds), Dynamic social network modeling and analysis: Workshop summary and papers National Academics Press.Google Scholar
Galaskiewicz, J. (1985). Social organization of an urban grants economy: A study of business philanthropy and non-profit organizations. Orlando, FL: Academic Press.Google Scholar
Glänzel, W., & Schubert, A. (2004). Analyzing scientific networks through co-authorship. Open Access publications from Katholieke Universiteit Leuven. Katholieke Universiteit Leuven.Google Scholar
Granovetter, M. S. (1973). The strength of weak ties. The American Journal of Sociology, 78 (6), 1360–1380.CrossRefGoogle Scholar
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. 109–118). Proceedings of the 4th annual acm web science conference. WebSci '12. New York, NY, USA: ACM.Google Scholar
Harary, F., & Kommel, H. J. (1979). Matrix measures for transitivity and balance. Journal of Mathematical Sociology, 6 (2), 199–210.Google Scholar
Hell, P. (1979). An introduction to the category of graphs. Topics in graph theory (New York, 1977) (pp. 120–136) Ann. New York Acad. Sci., vol. 328. New York: Acad. Sci.Google Scholar
Holland, P. W., & Leinhardt, S. (1971). Transitivity in structural models of small groups. Small Group Research, 2 (2), 107–124.Google Scholar
Kimberlin, C. L., & Winterstein, A. G. (2008). Validity and reliability of measurement instruments used in research. American Journal of Health-System Pharmacy, 65 (23), 2276–2284.Google Scholar
Kreher, D. L., & Stinson, D. R. (1999). Combinatorial algorithms: generation, enumeration, and search . SIGACT news, 30 (1), 33–35.Google Scholar
Lee, C., & Cunningham, P. (2014). Community detection: Effective evaluation on large social networks. Journal of Complex Networks, 2 (1), 19–37.Google Scholar
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.CrossRefGoogle Scholar
Lind, P. G., González, M. C., & Herrmann, H. J. (2005). Cycles and clustering in bipartite networks. Physical Review E, 72 (Nov), 056127.Google Scholar
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.Google Scholar
Mitchell, B. (1965). Theory of categories. Pure and Applied Mathematics, vol. 17. New York and London: Academic Press.Google Scholar
Newman, M. E. J. (2001). Scientific collaboration networks. I. Network construction and fundamental results. Physical Review E, 45 (2), 167–256 (electronic).Google Scholar
Newman, M. E. J. (2003). The structure and function of complex networks. SIAM Review, 45 (2), 167–256 (electronic).Google Scholar
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.Google Scholar
Opsahl, T. (2013). Triadic closure in two-mode networks: Redefining the global and local clustering coefficients. Social Networks, 35 (2), 159–167. Special Issue on Advances in Two-mode Social Networks.Google Scholar
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.Google Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Stanley, R. P. (2002). Enumerative combinatorics. Cambridge Studies in Advanced Mathematics, no. v. 1. Cambridge: Cambridge University Press.Google Scholar
Szabó, G., Alava, M., & Kertész, J. (2003). Structural transitions in scale-free networks. Physical Review E, 67 (5), 056102.Google Scholar
Uzzi, B., & Spiro, J. (2005). Collaboration and creativity: The small world problem. American Journal of Sociology, 111 (2), 447–504.Google Scholar
Vázquez, A. (2003). Growing network with local rules: Preferential attachment, clustering hierarchy, and degree correlations. Physical Review E, 67 (May), 056104.Google Scholar
Wasserman, S., & Faust, K. (1994). Social network analysis: Methods and applications. vol. 8. Cambridge: Cambridge university press.Google Scholar
Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of “small-world” networks. Nature, 393 (6684), 440–442.Google Scholar
Wickham, H. (2009). ggplot2: elegant graphics for data analysis. New York: Springer.Google Scholar
Supplementary material: PDF

Brunson supplementary material S1

Brunson supplementary material

Download Brunson supplementary material S1(PDF)
PDF 218.2 KB