= Link hypergraph
{title2=$\operatorname{lk}_H(v)=\{E\setminus\{v\}:v\in E\in\mathcal E(H)\}$}
The link at a fixed vertex $v$ of an $r$-<uniform hypergraph> has vertex set $V(H)\setminus\{v\}$ and the displayed $(r-1)$-element <hyperedges>. For a <universal countable uniform hypergraph>, its link has the <hypergraph extension property>: include $v$ in the finite set of vertices and prescribe only those $r$-edges containing $v$, completing the remaining prescription arbitrarily. Thus the link is a universal countable $(r-1)$-<uniform hypergraph>. In particular the link at a fixed vertex in the three-uniform case is the <Rado graph>. This operation retains a specified vertex; deleting the maximum from every edge is a different operation.
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