# Universality of the stochastic block model

arXiv: https://arxiv.org/abs/1806.04214 · HTML: https://mlsanity.com/paper/1806.04214/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2018.

## Built on by (most cited first, 5 of 5)

- [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)
- [Exact and rapid linear clustering of networks with dynamic programming](https://mlsanity.com/paper/2301.10403/) (2023)
- [From Leiden to Pleasure Island: The Constant Potts Model for Community Detection as a Hedonic Game](https://mlsanity.com/paper/2509.03834/) (2025)
- [The Spectral Barycentre of a Set of Graphs with Community Structure](https://mlsanity.com/paper/2502.00038/) (2025)

## Abstract (arXiv)

Mesoscopic pattern extraction (MPE) is the problem of finding a partition of the nodes of a complex network that maximizes some objective function. Many well-known network inference problems fall in this category, including, for instance, community detection, core-periphery identification, and imperfect graph coloring. In this paper, we show that the most popular algorithms designed to solve MPE problems can in fact be understood as special cases of the maximum likelihood formulation of the stochastic block model (SBM), or one of its direct generalizations. These equivalence relations show that the SBM is nearly universal with respect to MPE problems.