Skip to main content Accessibility help
×
Home
Hostname: page-component-747cfc64b6-nvdzj Total loading time: 0.355 Render date: 2021-06-14T15:26:53.012Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true }

Triadic analysis of affiliation networks

Published online by Cambridge University Press:  22 December 2015

JASON CORY BRUNSON
Affiliation:
Center for Quantitative Medicine, UConn Health, Farmington, CT 06030, USA (e-mail: brunson@uchc.edu)
Corresponding
E-mail address:

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.

Type
Research Article
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.

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), 121.CrossRefGoogle Scholar
Altman, D. G., & Bland, J. M. (1983). Measurement in medicine: The analysis of method comparison studies. The Statistician, 32 (3), 307317.CrossRefGoogle Scholar
Bonacich, P. (1991). Simultaneous group and individual centralities. Social Networks, 13 (2), 155168.CrossRefGoogle 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, 243269.CrossRefGoogle 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. 417433). London: SAGE Publications Ltd.Google Scholar
Breiger, R. L. (1974). The duality of persons and groups. Social Forces, 53 (2), 181190.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), 973998.CrossRefGoogle 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), 109120.CrossRefGoogle 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.CrossRefGoogle 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), 181187.CrossRefGoogle Scholar
de Sola Pool, I., & Kochen, M. (1978). Contacts and influence. Socnet, 1 (1), 551.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), 157191.CrossRefGoogle Scholar
Freeman, L. C. (1992). The sociological concept of “group”: An empirical test of two models. The American Journal of Sociology, 98 (1), 152166.CrossRefGoogle Scholar
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.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), 13601380.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. 109118). Proceedings of the 4th annual acm web science conference. WebSci '12. New York, NY, USA: ACM.CrossRefGoogle Scholar
Harary, F., & Kommel, H. J. (1979). Matrix measures for transitivity and balance. Journal of Mathematical Sociology, 6 (2), 199210.CrossRefGoogle Scholar
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.Google Scholar
Holland, P. W., & Leinhardt, S. (1971). Transitivity in structural models of small groups. Small Group Research, 2 (2), 107124.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), 22762284.CrossRefGoogle ScholarPubMed
Kreher, D. L., & Stinson, D. R. (1999). Combinatorial algorithms: generation, enumeration, and search . SIGACT news, 30 (1), 3335.CrossRefGoogle Scholar
Lee, C., & Cunningham, P. (2014). Community detection: Effective evaluation on large social networks. Journal of Complex Networks, 2 (1), 1937.CrossRefGoogle 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.Google Scholar
Lind, P. G., González, M. C., & Herrmann, H. J. (2005). Cycles and clustering in bipartite networks. Physical Review E, 72 (Nov), 056127.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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), 167256 (electronic).Google Scholar
Newman, M. E. J. (2003). The structure and function of complex networks. SIAM Review, 45 (2), 167256 (electronic).CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle 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 ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Uzzi, B., & Spiro, J. (2005). Collaboration and creativity: The small world problem. American Journal of Sociology, 111 (2), 447504.CrossRefGoogle Scholar
Vázquez, A. (2003). Growing network with local rules: Preferential attachment, clustering hierarchy, and degree correlations. Physical Review E, 67 (May), 056104.CrossRefGoogle ScholarPubMed
Wasserman, S., & Faust, K. (1994). Social network analysis: Methods and applications. vol. 8. Cambridge: Cambridge university press.CrossRefGoogle Scholar
Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of “small-world” networks. Nature, 393 (6684), 440442.CrossRefGoogle ScholarPubMed
Wickham, H. (2009). ggplot2: elegant graphics for data analysis. New York: Springer.CrossRefGoogle Scholar
Supplementary material: PDF

Brunson supplementary material S1

Brunson supplementary material

Download Brunson supplementary material S1(PDF)
PDF 218 KB
4
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Triadic analysis of affiliation networks
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Triadic analysis of affiliation networks
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Triadic analysis of affiliation networks
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *