Stochastic blockmodels for directed graphs.
Abstract
Holland and Leinhardt (1981) proposed the p 1 model for the analysis of binary directed graph data in network studies. Such a model provides information about the “attractiveness” and “expansiveness” of the individual nodes in the network, as well as the tendency of a pair of nodes to reciprocate relational ties. When the nodes are a priori partitioned into subgroups based on attributes such as race and sex, the density of ties from one subgroup to another can differ considerably from that relating another pair of subgroups, thus creating a situation called blocking in social networks. The p 1 model completely ignores this extra piece of information and is, therefore, unable to explain the block structure. Blockmodels that are simple extensions of the p 1 model are proposed specifically for such data. An iterative scaling algorithm is presented for fitting the model parameters by maximum likelihood. The methodology is illustrated in detail on two empirical examples.
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The group model, known as a stochastic block model in the statistical literature, was previously treated in a maximum-likelihood framework.
“The group model [12], known as a stochastic block model in the statistical literature [57], was previously treated in a maximum-likelihood framework.”
From Spatial Guilds in the Serengeti Food Web Revealed by a Bayesian Group Model (2011) · cites this paper as [57]
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“The group model [12], known as a stochastic block model in the statistical literature [57], was previously treated in a maximumlikelihood framework.”
Method
- Authors
- Wang, Y. J., & Wong, G. Y.
- Affiliations
- Rutgers, The State University of New Jersey (US)
- Memorial Sloan Kettering Cancer Center (US)
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1987-03
- Volume
- 82
- Issue
- 397
- Pages
- 8-19
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W1980347317
- Cited by
- 480
- References
- 26
- Citations by year
- 2026: 12 · 2025: 18 · 2024: 13 · 2023: 25 · 2022: 19 · 2021: 38 · 2020: 36 · 2019: 30 · 2018: 34 · 2017: 40 · 2016: 34 · 2015: 24 · 2014: 28 · 2013: 22 · 2012: 19
- FWCI
- 1.85
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the American Statistical Association (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Keywords
- stochastic block model, directed graphs, P1 model, blocking, reciprocity, iterative scaling, maximum likelihood estimation, social network analysis
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