# A Review of Stochastic Block Models and Extensions for Graph Clustering

arXiv: https://arxiv.org/abs/1903.00114 · HTML: https://mlsanity.com/paper/1903.00114/

## Key facts

- Cited by 46 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2019.

## Built on by (most cited first, 30 of 46)

- [A Survey of Community Detection Approaches: From Statistical Modeling to Deep Learning](https://mlsanity.com/paper/2101.01669/) (2021)
- [Synthetic Graph Generation to Benchmark Graph Learning](https://mlsanity.com/paper/2204.01376/) (2022)
- [Advancing Graph Generation through Beta Diffusion](https://mlsanity.com/paper/2406.09357/) (2024)
- [A Comprehensive Review of Community Detection in Graphs](https://mlsanity.com/paper/2309.11798/) (2023)
- [Partition and Code: learning how to compress graphs](https://mlsanity.com/paper/2107.01952/) (2021)
- [Using Embeddings for Causal Estimation of Peer Influence in Social Networks](https://mlsanity.com/paper/2205.08033/) (2022)
- [Learning on Large Graphs using Intersecting Communities](https://mlsanity.com/paper/2405.20724/) (2024)
- [The effect of network topologies on fully decentralized learning: a preliminary investigation](https://mlsanity.com/paper/2307.15947/) (2023)
- [Impact of network topology on the performance of Decentralized Federated Learning](https://mlsanity.com/paper/2402.18606/) (2024)
- [Supra-Laplacian Encoding for Transformer on Dynamic Graphs](https://mlsanity.com/paper/2409.17986/) (2024)
- [Sparse Subspace Clustering in Diverse Multiplex Network Model](https://mlsanity.com/paper/2206.07602/) (2022)
- [A Comprehensive Survey on Graph Summarization with Graph Neural Networks](https://mlsanity.com/paper/2302.06114/) (2023)
- [Differentially private exact recovery for stochastic block models](https://mlsanity.com/paper/2406.02644/) (2024)
- [Symmetrical SyncMap for Imbalanced General Chunking Problems](https://mlsanity.com/paper/2310.10045/) (2023)
- [Semi-Supervised Clustering with Inaccurate Pairwise Annotations](https://mlsanity.com/paper/2104.02146/) (2021)
- [Alignment and Comparison of Directed Networks via Transition Couplings of Random Walks](https://mlsanity.com/paper/2106.07106/) (2021)
- [Restricted Tweedie Stochastic Block Models](https://mlsanity.com/paper/2310.10952/) (2023)
- [Large Generative Graph Models](https://mlsanity.com/paper/2406.05109/) (2024)
- [flow-based clustering and spectral clustering: a comparison](https://mlsanity.com/paper/2206.10019/) (2022)
- [Containing a spread through sequential learning: to exploit or to explore?](https://mlsanity.com/paper/2303.00141/) (2023)
- [Inference and Visualization of Community Structure in Attributed Hypergraphs Using Mixed-Membership Stochastic Block Models](https://mlsanity.com/paper/2401.00688/) (2024)
- [Advanced Graph Clustering Methods: A Comprehensive and In-Depth Analysis](https://mlsanity.com/paper/2407.09055/) (2024)
- [Estimating the number of clusters of a Block Markov Chain](https://mlsanity.com/paper/2407.18287/) (2024)
- [A Dirichlet stochastic block model for composition-weighted networks](https://mlsanity.com/paper/2408.00651/) (2024)
- [PieClam: A Universal Graph Autoencoder Based on Overlapping Inclusive and Exclusive Communities](https://mlsanity.com/paper/2409.11618/) (2024)
- [Deep Graph Learning will stall without Network Science](https://mlsanity.com/paper/2502.01177/) (2025)
- [Are GNNs doomed by the topology of their input graph?](https://mlsanity.com/paper/2502.17739/) (2025)
- [Relational Database Distillation: From Structured Tables to Condensed Graph Data](https://mlsanity.com/paper/2510.06980/) (2025)
- [Statistical embedding: Beyond principal components](https://mlsanity.com/paper/2106.01858/) (2021)
- [Identifying bias in cluster quality metrics](https://mlsanity.com/paper/2112.06287/) (2021)

## Abstract (arXiv)

There have been rapid developments in model-based clustering of graphs, also known as block modelling, over the last ten years or so. We review different approaches and extensions proposed for different aspects in this area, such as the type of the graph, the clustering approach, the inference approach, and whether the number of groups is selected or estimated. We also review models that combine block modelling with topic modelling and/or longitudinal modelling, regarding how these models deal with multiple types of data. How different approaches cope with various issues will be summarised and compared, to facilitate the demand of practitioners for a concise overview of the current status of these areas of literature.