# β models for random hypergraphs with a given degree sequence

arXiv: https://arxiv.org/abs/1407.1004 · HTML: https://mlsanity.com/paper/1407.1004/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2014.

## Built on by (most cited first, 4 of 4)

- [Nonparametric Modeling of Higher-Order Interactions via Hypergraphons](https://mlsanity.com/paper/2105.08678/) (2021)
- [Core-periphery Models for Hypergraphs](https://mlsanity.com/paper/2206.00783/) (2022)
- [Degree Heterogeneity in Higher-Order Networks: Inference in the Hypergraph boldsymbolβ-Model](https://mlsanity.com/paper/2307.02818/) (2023)
- [Privacy utility trade offs for parameter estimation in degree heterogeneous higher order networks](https://mlsanity.com/paper/2602.03948/) (2026)

## Abstract (arXiv)

We introduce the beta model for random hypergraphs in order to represent the occurrence of multi-way interactions among agents in a social network. This model builds upon and generalizes the well-studied beta model for random graphs, which instead only considers pairwise interactions. We provide two algorithms for fitting the model parameters, IPS (iterative proportional scaling) and fixed point algorithm, prove that both algorithms converge if maximum likelihood estimator (MLE) exists, and provide algorithmic and geometric ways of dealing the issue of MLE existence.