# Stochastic Block Models are a Discrete Surface Tension

arXiv: https://arxiv.org/abs/1806.02485 · HTML: https://mlsanity.com/paper/1806.02485/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jun 2018.

## Built on by (most cited first, 3 of 3)

- [Generative hypergraph clustering: from blockmodels to modularity](https://mlsanity.com/paper/2101.09611/) (2021)
- [On the existence of solutions to adversarial training in multiclass classification](https://mlsanity.com/paper/2305.00075/) (2023)
- [Modularity maximisation for graphons](https://mlsanity.com/paper/2101.00503/) (2021)

## Abstract (arXiv)

Networks, which represent agents and interactions between them, arise in myriad applications throughout the sciences, engineering, and even the humanities. To understand large-scale structure in a network, a common task is to cluster a network's nodes into sets called "communities", such that there are dense connections within communities but sparse connections between them. A popular and statistically principled method to perform such clustering is to use a family of generative models known as stochastic block models (SBMs). In this paper, we show that maximum likelihood estimation in an SBM is a network analog of a well-known continuum surface-tension problem that arises from an application in metallurgy. To illustrate the utility of this relationship, we implement network analogs of three surface-tension algorithms, with which we successfully recover planted community structure in synthetic networks and which yield fascinating insights on empirical networks that we construct from hyperspectral videos.