Sender- and Receiver-specific blockmodels


Share / Export Citation / Email / Print / Text size:

Journal of Social Structure

International Network for Social Network Analysis

Subject: Social Sciences


eISSN: 1529-1227





Volume / Issue / page

Volume 22 (2021)
Volume 21 (2020)
Volume 20 (2019)
Volume 19 (2018)
Volume 18 (2017)
Volume 17 (2016)
Volume 16 (2015)
Volume 15 (2014)
Volume 14 (2013)
Volume 13 (2012)
Volume 12 (2011)
Volume 11 (2010)
Volume 10 (2009)
Related articles

VOLUME 16 , ISSUE 1 (December 2015) > List of articles

Sender- and Receiver-specific blockmodels

Zhi Geng / Krzysztof Nowicki *

Keywords : Directed graph, Blockmodeling, Out-nets, In-nets, Ego-nets, EM algorithm, Multinomial distribution

Citation Information : Journal of Social Structure. Volume 16, Issue 1, Pages 1-34, DOI:

License : (CC BY-NC 4.0)

Published Online: 13-August-2019



We propose a sender-specific blockmodel for network data which utilizes both the group membership and the identities of the vertices. This is accomplished by introducing the edge probabilities (θi,v) for 1 ≤ i ≤ c, 1 ≤ v ≤ n, where i specifies the group membership of a sending vertex and v specifies the identity of the receiving vertex. In addition, group membership is consider to be random, with parameters (Pi)ic=1·We present methods based on the EM algorithm for the parameter estimations and discuss the recovery of latent group memberships. A companion model, the receiver-specific blockmodel, is also introduced in which the edge probabilities (ψu,j) for 1 ≤ u ≤ n, 1 ≤ j ≤ c depend on the membership of a vertex receiving a directed edge. We apply both models to several sets of social network data.

Content not available PDF Share



  1. Andersen, E. B. (1980). Discrete Statistical Models with Social Science Applications. NorthHolland, Amsterdam.
  2. Boer, P., Huisman, M., Snijders, T. and Zeggelink, E.P.H. (2003). StOCNET: an open software system for the advanced statistical analysis of social networks. Version 1.4. Groningen: ProGAMMA / ICS.
  3. Burnham, K. P. and Anderson, D. R. (2002). Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach (2nd ed.). Springer-Verlag, ISBN 0-387-95364-7.
  4. Crossley, N., Bellotti, E., Edwards, G., Everett, M. G., Koskinen, J. and Tranmer, M. (2015) Social Network Analysis, An Actor Centred Approach. Sage Publications Ltd, ISBN: 9781446267769.
  5. Dampster, A.P., Laird, N.M. and Rubin, D.B. (1977). Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society, B (39):1-38.
  6. Daudin, J. Picard, F. and Robin, S. (2008). A mixture model for random graph. Statistics and computing (18):173-183.
  7. Hansell, S. (1984). Cooperative groups, weak ties, and the integration of peer friendships. Social Psychology Quarterly, 47, 316-328.
  8. Kaiser, M. (2008). Mean clustering coefficients: the role of isolated nodes and leafs on clustering measures for small-world networks. New J. Phys. 10 083042.
  9. Kaiser, M. (2008). Mean clustering coefficients: the role of isolated nodes and leafs on clustering measures for small-world networks. New J. Phys. 10 083042.
  10. Krackhardt, D. (1987). Cognitive social structures. Social Networks, 9, 104-134.
  11. Luce, R.D. and Perry, A.D. (1949). A method of matrix analysis of group structure. Psychometrika 14 (1): 95-116.                                                                                                       
  12. Newman, M. (2006). Finding community structure in networks using the eigenvectors of matrices. Phys. Rev. E 74, 036104.
  13. Newman, M. and Leicht, E. (2007). Mixture models and exploratory analysis in networks. PNAS 104:9564-9569.
  14. Nowicki, K. and Snijders, T. (2001). Estimation and prediction for stochastic blockstructures. J. Amer. Statist. Assoc., 96(455):1077-1087.
  15. Picard, F. (2008). An Introduction to mixture models. SSB preprint(7).
  16. Snijders, T. and Nowicki, K. (1997). Estimation and prediction for stochastic blockmodels for graphs with latent block structure. Journal of Classification, 14, 75 -100.
  17. Wasserman, S. and Faust, K. (1994). Social Network Analysis: Methods and Application. Cambridge: Cambridge University Press.
  18. G. B. Folland. Higher-Order Derivatives and Taylor’s Formula in Several Variables.
  19. Watts, D.J. and Strogatz, S.H. (1998). Collective dynamics of ’smallworld’ networks. Nature 393 (6684): 440-442.
  20. Yang, Y. (2005). Can the strengths of AIC and BIC be shared?. Biometrika 92: 937-950.
  21. Zachary, W. (1977). An information ow model for conflict and fission in small groups. Journal of Anthropological Research 33, 452-473.