# Community detection in the sparse hypergraph stochastic block model

## TL;DR

This paper proves the existence of a sharp threshold for community detection in sparse hypergraph stochastic block models and introduces a spectral algorithm that effectively identifies communities above this threshold.

## Contribution

It confirms the conjecture for two blocks and extends spectral methods from graphs to hypergraphs for community detection.

## Key findings

- Spectral algorithm successfully detects communities above the threshold.
- The paper confirms the conjecture for the two-block case.
- Extension of spectral methods from graphs to hypergraphs.

## Abstract

We consider the community detection problem in sparse random hypergraphs. Angelini et al. (2015) conjectured the existence of a sharp threshold on model parameters for community detection in sparse hypergraphs generated by a hypergraph stochastic block model. We solve the positive part of the conjecture for the case of two blocks: above the threshold, there is a spectral algorithm which asymptotically almost surely constructs a partition of the hypergraph correlated with the true partition. Our method is a generalization to random hypergraphs of the method developed by Massouli\'{e} (2014) for sparse random graphs.