# The HyperKron Graph Model for higher-order features

arXiv: https://arxiv.org/abs/1809.03488 · HTML: https://mlsanity.com/paper/1809.03488/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2018.

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

- [Core-periphery Models for Hypergraphs](https://mlsanity.com/paper/2206.00783/) (2022)

## Abstract (arXiv)

Graph models have long been used in lieu of real data which can be expensive and hard to come by. A common class of models constructs a matrix of probabilities, and samples an adjacency matrix by flipping a weighted coin for each entry. Examples include the ErdHos-R'enyi model, Chung-Lu model, and the Kronecker model. Here we present the HyperKron Graph model: an extension of the Kronecker Model, but with a distribution over hyperedges. We prove that we can efficiently generate graphs from this model in order proportional to the number of edges times a small log-factor, and find that in practice the runtime is linear with respect to the number of edges. We illustrate a number of useful features of the HyperKron model including non-trivial clustering and highly skewed degree distributions. Finally, we fit the HyperKron model to real-world networks, and demonstrate the model's flexibility with a complex application of the HyperKron model to networks with coherent feed-forward loops.