# Bayesian stochastic blockmodeling

arXiv: https://arxiv.org/abs/1705.10225 · HTML: https://mlsanity.com/paper/1705.10225/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2017.

## Built on by (most cited first, 27 of 27)

- [SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators](https://mlsanity.com/paper/2204.01613/) (2022)
- [Generative hypergraph clustering: from blockmodels to modularity](https://mlsanity.com/paper/2101.09611/) (2021)
- [Scholastic: Graphical Human-Al Collaboration for Inductive and Interpretive Text Analysis](https://mlsanity.com/paper/2208.06133/) (2022)
- [Partition and Code: learning how to compress graphs](https://mlsanity.com/paper/2107.01952/) (2021)
- [Disentangling homophily, community structure and triadic closure in networks](https://mlsanity.com/paper/2101.02510/) (2021)
- [Estimating Social Influence from Observational Data](https://mlsanity.com/paper/2204.01633/) (2022)
- [Network reconstruction via the minimum description length principle](https://mlsanity.com/paper/2405.01015/) (2024)
- [Neural-prior stochastic block model](https://mlsanity.com/paper/2303.09995/) (2023)
- [RelDiff: Relational Data Generative Modeling with Graph-Based Diffusion Models](https://mlsanity.com/paper/2506.00710/) (2025)
- [Multilayer Networks for Text Analysis with Multiple Data Types](https://mlsanity.com/paper/2106.15821/) (2021)
- [Descriptive vs. inferential community detection in networks: pitfalls, myths, and half-truths](https://mlsanity.com/paper/2112.00183/) (2021)
- [Implicit models, latent compression, intrinsic biases, and cheap lunches in community detection](https://mlsanity.com/paper/2210.09186/) (2022)
- [Estimation of partial rankings from sparse, noisy comparisons](https://mlsanity.com/paper/2501.02505/) (2025)
- [Semi-Supervised Clustering with Inaccurate Pairwise Annotations](https://mlsanity.com/paper/2104.02146/) (2021)
- [Systematic assessment of the quality of fit of the stochastic block model for empirical networks](https://mlsanity.com/paper/2201.01658/) (2022)
- [Consistency between ordering and clustering methods for graphs](https://mlsanity.com/paper/2208.12933/) (2022)
- [Symmetry-driven embedding of networks in hyperbolic space](https://mlsanity.com/paper/2406.10711/) (2024)
- [Deep Graph Learning will stall without Network Science](https://mlsanity.com/paper/2502.01177/) (2025)
- [Robustness modularity in complex networks](https://mlsanity.com/paper/2110.02297/) (2021)
- [An adaptation of InfoMap to absorbing random walks using absorption-scaled graphs](https://mlsanity.com/paper/2112.10953/) (2021)
- [A Simple Quantum Blockmodeling with Qubits and Permutations](https://mlsanity.com/paper/2311.07726/) (2023)
- [Learning dynamic representations of the functional connectome in neurobiological networks](https://mlsanity.com/paper/2402.14102/) (2024)
- [Siamese Neural Network for Label-Efficient Critical Phenomena Prediction in 3D Percolation Models](https://mlsanity.com/paper/2507.14159/) (2025)
- [Large Scale Community-Aware Network Generation](https://mlsanity.com/paper/2511.19717/) (2025)
- [Graph energy as a measure of community detectability in networks](https://mlsanity.com/paper/2601.05065/) (2026)
- [Scalable inference of spatial regions and temporal signatures from time series](https://mlsanity.com/paper/2605.05008/) (2026)
- [Accelerating Dynamic Graph Clustering on GPU Architectures with cuGraph](https://mlsanity.com/paper/2608.03695/) (2026)

## Abstract (arXiv)

This chapter provides a self-contained introduction to the use of Bayesian inference to extract large-scale modular structures from network data, based on the stochastic blockmodel (SBM), as well as its degree-corrected and overlapping generalizations. We focus on nonparametric formulations that allow their inference in a manner that prevents overfitting, and enables model selection. We discuss aspects of the choice of priors, in particular how to avoid underfitting via increased Bayesian hierarchies, and we contrast the task of sampling network partitions from the posterior distribution with finding the single point estimate that maximizes it, while describing efficient algorithms to perform either one. We also show how inferring the SBM can be used to predict missing and spurious links, and shed light on the fundamental limitations of the detectability of modular structures in networks.