# Construction of and efficient sampling from the simplicial configuration model

arXiv: https://arxiv.org/abs/1705.10298 · HTML: https://mlsanity.com/paper/1705.10298/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2017.

## Built on by (most cited first, 2 of 2)

- [Inference of hyperedges and overlapping communities in hypergraphs](https://mlsanity.com/paper/2204.05646/) (2022)
- [Learning physical properties of anomalous random walks using graph neural networks](https://mlsanity.com/paper/2103.11738/) (2021)

## Abstract (arXiv)

Simplicial complexes are now a popular alternative to networks when it comes to describing the structure of complex systems, primarily because they encode multi-node interactions explicitly. With this new description comes the need for principled null models that allow for easy comparison with empirical data. We propose a natural candidate, the simplicial configuration model. The core of our contribution is an efficient and uniform Markov chain Monte Carlo sampler for this model. We demonstrate its usefulness in a short case study by investigating the topology of three real systems and their randomized counterparts (using their Betti numbers). For two out of three systems, the model allows us to reject the hypothesis that there is no organization beyond the local scale.