# A class of models for random hypergraphs

arXiv: https://arxiv.org/abs/2210.12698 · HTML: https://mlsanity.com/paper/2210.12698/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2022.

## Built on by (most cited first, 1 of 1)

- [Inference and Visualization of Community Structure in Attributed Hypergraphs Using Mixed-Membership Stochastic Block Models](https://mlsanity.com/paper/2401.00688/) (2024)

## Abstract (arXiv)

Despite the recently exhibited importance of higher-order interactions for various processes, few flexible (null) models are available. In particular, most studies on hypergraphs focus on a small set of theoretical models. Here, we introduce a class of models for random hypergraphs which displays a similar level of flexibility of complex network models and where the main ingredient is the probability that a node belongs to a hyperedge. When this probability is a constant, we obtain a random hypergraph in the same spirit as the Erdos-Renyi graph. This framework also allows us to introduce different ingredients such as the preferential attachment for hypergraphs, or spatial random hypergraphs. In particular, we show that for the Erdos-Renyi case there is a transition threshold scaling as 1/√EN where N is the number of nodes and E the number of hyperedges. We also discuss a random geometric hypergraph which displays a percolation transition for a threshold distance scaling as rc^*~ 1/√E. For these various models, we provide results for the most interesting measures, and also introduce new ones in the spatial case for characterizing the geometrical properties of hyperedges. These different models might serve as benchmarks useful for analyzing empirical data.