Stochastic blockmodels: First steps

By Paul Holland, Kathryn B. Laskey, S. Leinhardt. 1983

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Citations in the corpus

Community detection in graphs (2009, background): “In this case, vertices are organized in classes such that the linking probabilities of a vertex with all other vertices of the graph are the same for vertices in the same class, which are called stochastically equivalent (Fienberg and Wasserman, 1981; Holland et al., 1983).”
A Review of Relational Machine Learning for Knowledge Graphs (2015, background): “This refers to the property where entities can be divided into distinct groups (blocks), such that all the members of a group have similar relationships to members of other groups [58]–[60].”
Graph Embedding Techniques, Applications, and Performance: A Survey (2017, background): “Generating synthetic networks with realworld characteristics has been a popular field of research[100] primarily for ease of simulations.”
Consistency of maximum-likelihood and variational estimators in the Stochastic Block Model (2011, methodology): “Mixture models for random graphs were first proposed by Holland et al. (1983) who defined the so-called stochastic block model (SBM), in reference to an older non stochastic block model widely used in social science.”
Limit theorems for eigenvectors of the normalized Laplacian for random graphs (2016, background): “Random dot product graphs are related to stochastic block model graphs [20] and degree-corrected stochastic imsart-aos ver.”
Estimation and Prediction for Stochastic Blockstructures (2001, background): “Fienberg and Wasserman (1981) and Holland, Laskey, and Leinhardt (1983) generalized the deterministic concept of structural equivalence to probabilistic models.”
A Proof of the Block Model Threshold Conjecture (2013, background): “At the same time, the model is a classical statistical model for networks with communities [15], and the questions of identiﬁability of the parameters and recovery of the clusters have been studied extensively, see e.g. [26,2,24].”
Community detection and stochastic block models: recent developments (2017, methodology): “Chen (2014), two unbalanced13 communities Neeman and Netrapalli (2014), and a single community Montanari (2015).”
Latent Space Approaches to Social Network Analysis (2002, methodology): “These data are standard in the social network analysis literature, having been modeled by Holland and Leinhardt (1981), Reitz (1982), Holland, Laskey, and Leinhardt (1983), and Fienberg et al. (1981).”
p2: a random effects model with covariates for directed graphs (2004, methodology): “This idea is further developed in the so-called a priori stochastic blockmodels introduced in HOLLAND, LASKEY, and LEINHARDT (1983) and in a direct extension of the p1 model by WANG and WONG (1987).”
Exact Recovery in the Stochastic Block Model (2014, background): “More specifically, the stochastic block model has been at the center of the attention in a large body of literature [14]–[16], [19], [24], [26], [29], [30], [32], [33], [35], [38], [39], as a testbed for algorithms (see [10] for a survey) as well as a scalable model for large data sets (see [22] and”
Community Detection in General Stochastic Block models: Fundamental Limits and Efficient Algorithms for Recovery (2015, methodology): “Recently, similar phenomena have been identified for the stochastic block model (SBM), one of the most popular network models exhibiting community structures [20], [21], [22], [23], [24], [25].”
Consistency of spectral clustering in stochastic block models (2013, methodology): “Among the many existing statistical models for network data, the stochastic block model, hence-forth SBM, of Holland et al. (1983) stands out for both its simplicity and expressive power.”