Fix a positive integer $n$, a real number $p\in (0,1]$, and a (perhaps random) hypergraph $\mathcal{H}$ on $[n]$. We introduce and investigate the following random multigraph model, which we denote $\mathbb{G}(n,p\, ; \,\mathcal{H})$: begin with an empty graph on $n$ vertices, which are labelled by the set $[n]$. For every $H\in \mathcal{H}$ choose, independently from previous choices, a doubleton from $H$, say $D = \{i,j\} \subset H$, uniformly at random and then introduce an edge between the vertices $i$ and $j$ in the graph with probability $p$, where each edge is introduced independently of all other edges.

翻译：固定正整数 $n$、实数 $p\in(0,1]$ 以及（可能随机的）超图 $\mathcal{H}$（顶点集为 $[n]$）。我们引入并研究以下随机多重图模型，记作 $\mathbb{G}(n,p\, ; \,\mathcal{H})$：从 $n$ 个顶点（标记为集合 $[n]$）的空图开始。对于每个 $H\in \mathcal{H}$，独立于先前选择，从 $H$ 中均匀随机选取一个二元组（记作 $D = \{i,j\} \subset H$），随后以概率 $p$ 在顶点 $i$ 与 $j$ 之间引入一条边，其中每条边的引入独立于其他所有边。