High-order structures have been recognised as suitable models for systems going beyond the binary relationships for which graph models are appropriate. Despite their importance and surge in research on these structures, their random cases have been only recently become subjects of interest. One of these high-order structures is the oriented hypergraph, which relates couples of subsets of an arbitrary number of vertices. Here we develop the Erd\H{o}s-R\'enyi model for oriented hypergraphs, which corresponds to the random realisation of oriented hyperedges of the complete oriented hypergraph. A particular feature of random oriented hypergraphs is that the ratio between their expected number of oriented hyperedges and their expected degree or size is 3/2 for large number of vertices. We highlight the suitability of oriented hypergraphs for modelling large collections of chemical reactions and the importance of random oriented hypergraphs to analyse the unfolding of chemistry.

翻译：高阶结构已被认为是超越二元关系（图模型适用于此类关系）的系统之合适模型。尽管这些结构具有重要性且相关研究激增，其随机情形直到最近才成为关注焦点。其中一种高阶结构是定向超图，它关联任意数量顶点子集的配对。本文针对定向超图发展了Erdős-Rényi模型，该模型对应于完全定向超图中定向超边的随机实现。随机定向超图的一个显著特征是：当顶点数较大时，其定向超边期望数与期望度数或规模之比为3/2。我们强调了定向超图在建模大量化学反应集合方面的适用性，以及随机定向超图在分析化学演化过程中的重要性。