Connectivity of Random Geometric Hypergraphs

TL;DR

This paper studies the connectivity of a new random geometric hypergraph model that captures higher order relationships, providing conditions on the radius for ensuring the hypergraph's connectivity as the size grows.

Contribution

It introduces a novel hypergraph model based on bipartite graphs and analyzes its connectivity properties in the asymptotic regime.

Findings

Provides a radius condition for connectivity in the model.

Shows the model captures higher order data relationships.

Analyzes asymptotic behavior of the hypergraph connectivity.

Abstract

We consider a random geometric hypergraph model based on an underlying bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a node is assigned to those hyperedges that lie with a certain radius. From a modelling perspective, we explain how the model captures higher order connections that arise in real data sets. Our main contribution is to study the connectivity properties of the model. In an asymptotic limit where the number of nodes and hyperedges grow in tandem we give a condition on the radius that guarantees connectivity.