Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-23T09:30:15.639Z Has data issue: false hasContentIssue false
  • English
  • Français

Clustering ensembles of social networks

Published online by Cambridge University Press:  15 April 2019

Tracy M. Sweet Open the ORCID record for Tracy M. Sweet [Opens in a new window] ,
Abby Flynt  and
David Choi
Tracy M. Sweet*
Affiliation:
Department of Human Development and Quantitative MethodologyUniversity of Maryland College Park, MD, USA
Abby Flynt
Affiliation:
Department of MathematicsBucknell University Lewisburg, PA, USA
David Choi
Affiliation:
Heinz College Carnegie Mellon University Pittsburgh, PA, USA
*
*Corresponding author. Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Recently there has been significant work in the social sciences involving ensembles of social networks, that is, multiple, independent, social networks such as students within schools or employees within organizations. There remains, however, very little methodological work on exploring these types of data structures. We present methods for clustering social networks with observed nodal class labels, based on statistics of walk counts between the nodal classes. We extend this method to consider only non-backtracking walks, and introduce a method for normalizing the counts of long walk sequences using those of shorter ones. We then present a method for clustering networks based on these statistics to explore similarities among networks. We demonstrate the utility of this method on simulated network data, as well as on advice-seeking networks in education.

Keywords

clusteringgraph kernelrandom walksadvice networkseducation
Type
Original Article
Information
Network Science , Volume 7 , Issue 2 , June 2019 , pp. 141 - 159
Copyright
© Cambridge University Press 2019 

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

Everitt, B., Landau, S., Leese, M., & Stahl, D. (2011). Cluster analysis. Wiley Series in Probability and Statistics. Hoboken: John Wiley & Sons.CrossRefGoogle Scholar
Faust, K., & Skvoretz, J. (2002). Comparing networks across space and time, size and species. Sociological Methodology, 32, 267–299.CrossRefGoogle Scholar
Fraley, C., & Raftery, A. E. (2002). Model-based clustering, discriminant analysis, and density estimation. Journal of the American statistical Association, 97, 611–631.CrossRefGoogle Scholar
Frank, K. A., Lo, Y.-J., & Sun, M. (2014). Social network analysis of the influences of educational reforms on teachers practices and interactions. Zeitschrift für Erziehungswissenschaft, 17, 117–134.CrossRefGoogle Scholar
Frank, K. A., Zhao, Y., & Borman, K. (2004). Social capital and the diffusion of innovations within organizations: The case of computer technology in schools. Sociology of Education, 77, 148–171.CrossRefGoogle Scholar
Friedman, J., Hastie, T., & Tibshirani, R. (2001). The elements of statistical learning (vol. 1). New York: Springer.Google Scholar
Gest, S. D., & Rodkin, P. C. (2011). Teaching practices and elementary classroom peer ecologies. Journal of Applied Developmental Psychology, 32, 288–296.CrossRefGoogle Scholar
Harris, A. (2009). Distributed leadership: What we know. In Distributed leadership (pp. 11–21). Dordrecht: Springer.CrossRefGoogle Scholar
Harris, A., & Spillane, J. (2008). Distributed leadership through the looking glass. Management in Education, 22, 31–34.CrossRefGoogle Scholar
Harris, K., Halpern, C., Whitsel, E., Hussey, J., Tabor, J., Entzel, P., & Udry, J. (2009). The national longitudinal study of adolescent health. Research design. Retrieved from http://www.cpc.unc.edu/projects/addhealth/design (September 2011).Google Scholar
Hashimoto, K.-i. (1989). Zeta functions of finite graphs and representations of p-adic groups. Automorphic Forms and Geometry of Arithmetic Varieties, 15, 211–280.Google Scholar
Holland, P., Laskey, K., & Leinhardt, S. (1983). Stochastic blockmodels: First steps. Social Networks, 5, 109–137.CrossRefGoogle Scholar
Hopkins, M., Lowenhaupt, R., & Sweet, T. M. (2015). Organizing instruction in new immigrant destinations: District infrastructure and subject-specific school practice. American Educational Research Journal, 52, 408–439.CrossRefGoogle Scholar
Hubert, L. & Arabie, P. (1985). Comparing partitions. Journal of Classification, 2, 193–218.CrossRefGoogle Scholar
Kashima, H., Tsuda, K., & Inokuchi, A. (2003). Menlo Park: AAAI Press. Marginalized kernels between labeled graphs. In Proceedings of the 20th international conference on machine learning (ICML-03) (pp. 321–328).Google Scholar
Krzakala, F., Moore, C., Mossel, E., Neeman, J., Sly, A., Zdeborová, L., & Zhang, P. (2013). Spectral redemption in clustering sparse networks. Proceedings of the National Academy of Sciences, 110, 20935–20940.CrossRefGoogle ScholarPubMed
Lazega, E., & Snijders, T. A. (2015). Multilevel network analysis for the social sciences: Theory, methods and applications (vol. 12). Berlin, Germany: Springer.Google Scholar
MacQueen, J., (1967). Some methods for classification and analysis of multivariate observations. In Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, Oakland, CA, USA (vol. 1, pp. 281–297). Berkeley: University of California Press.Google Scholar
Maechler, M., Rousseeuw, P., Struyf, A., Hubert, M., & Hornik, K. (2018). cluster: Cluster analysis basics and extensions.Google Scholar
Martin, T., Zhang, X., & Newman, M. (2014). Localization and centrality in networks. Physical Review E, 90, 052808.CrossRefGoogle ScholarPubMed
Paluck, E. L., & Shepherd, H. (2012). The salience of social referents: A field experiment of collective norms and harassment behavior in a school social network. Journal of Personality and Social Psychology, 103, 899–915.CrossRefGoogle Scholar
Ralaivola, L., Swamidass, S. J., Saigo, H., & Baldi, P. (2005). Graph kernels for chemical informatics. Neural Networks, 18, 1093–1110.CrossRefGoogle ScholarPubMed
Saigo, H., Nowozin, S., Kadowaki, T., Kudo, T., & Tsuda, K. (2009). gBoost: A mathematical programming approach to graph classification and regression. Machine Learning, 75, 69–89.CrossRefGoogle Scholar
Sarkar, A., Fienberg, S., & Krackhardt, D. (2010). Predicting profitability using advice branch bank networks. Statistical Methodology, 7, 429–444.CrossRefGoogle Scholar
Sinani, E., Stafsudd, A., Thomsen, S., Edling, C., & Randøy, T. (2008). Corporate governance in Scandinavia: Comparing networks and formal institutions. European Management Review, 5, 27–40.CrossRefGoogle Scholar
Snijders, T., & Kenny, D. (1999). The social relations model for family data: A multilevel approach. Personal Relationships, 6, 471–486.CrossRefGoogle Scholar
Snijders, T. A., & Baerveldt, C. (2003). A multilevel network study of the effects of delinquent behavior on friendship evolution. Journal of Mathematical Sociology, 27, 123–151.CrossRefGoogle Scholar
Snijders, T. A., Steglich, C. E., Schweinberger, M., & Huisman, M. (2008). Manual for SIENA version 3.2. Department of Sociology, ICS, University of Groningen, Groningen, The Netherlands.Google Scholar
Spillane, J., Hopkins, M., & Sweet, T. (2015). Intra- and inter-school instructional interactions: Exploring conditions for instructional knowledge production within and between schools. American Journal of Education, 122, 71–110.CrossRefGoogle Scholar
Spillane, J. P. (2012). Distributed leadership (vol. 4). San Francisco: John Wiley & Sons.Google Scholar
Spillane, J. P., Halverson, R., & Diamond, J. B. (2001). Investigating school leadership practice: A distributed perspective. Educational Researcher, 30, 23–28.CrossRefGoogle Scholar
Spillane, J. P., & Hopkins, M. (2013). Organizing for instruction in education systems and school organizations: How the subject matters. Journal of Curriculum Studies, 45, 721–747.CrossRefGoogle Scholar
Spillane, J. P., Hopkins, M., & Sweet, T. M. (2016). Exploring the relationship between teachers’ instructional ties and teachers’ instructional beliefs: Trying not to ‘put the cart before the horse’. American Journal of Education, 122, 71–110.CrossRefGoogle Scholar
Spillane, J. P., Shirrell, M., & Sweet, T. M. (2017). The elephant in the schoolhouse: The role of propinquity in school staff interactions about teaching. Sociology of Education, 90, 149–171.CrossRefGoogle Scholar
Sweet, T., & Zheng, Q. (2017). A mixed membership model-based measure for subgroup integration in social networks. Social Networks, 48, 169–180.CrossRefGoogle Scholar
Sweet, T. M., Thomas, A. C., & Junker, B. W. (2013). Hierarchical network models for education research: Hierarchical latent space models. Journal of Educational and Behavioral Statistics, 38, 295–318.CrossRefGoogle Scholar
Tibshirani, R., Walther, G., & Hastie, T. (2001). Estimating the number of clusters in a data set via the gap statistic. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 63, 411–423.CrossRefGoogle Scholar
Traud, A. L., Kelsic, E. D., Mucha, P. J., & Porter, M. A. (2011). Comparing community structure to characteristics in online collegiate social networks. SIAM Review, 53, 526–543.CrossRefGoogle Scholar
Vishwanathan, S. V. N., Schraudolph, N. N., Kondor, R., & Borgwardt, K. M. (2010). Graph kernels. Journal of Machine Learning Research, 11, 1201–1242.Google Scholar
Vogelstein, J. T., Roncal, W. G., Vogelstein, R. J., & Priebe, C. E. (2013). Graph classification using signal-subgraphs: Applications in statistical connectomics. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35, 1539–1551.CrossRefGoogle ScholarPubMed
Ward, J. H. Jr. (1963). Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association, 58, 236–244.CrossRefGoogle Scholar
Wolfe, J. H. (1963). Object cluster analysis of social areas, Ph.D. thesis, University of California.Google Scholar
Zijlstra, B., van Duijn, M., & Snijders, T. (2006). The multilevel p2 model. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 2, 42–47.CrossRefGoogle Scholar
Žnidaršič, A., Ferligoj, A., & Doreian, P. (2017). Actor non-response in valued social networks: The impact of different non-response treatments on the stability of blockmodels. Social Networks, 48, 46–56.CrossRefGoogle Scholar