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.

翻译：我们考虑一种基于底层二分图的随机几何超图模型。节点与超边在区域内均匀采样，且节点被分配至位于特定半径内的超边中。从建模角度，我们阐释了该模型如何捕捉真实数据集中出现的高阶连接关系。我们的主要贡献在于研究该模型的连通性质。在节点与超边数量同步增长的渐近极限下，我们给出了确保连通性所需的半径条件。