= Rado graph
{c}
{title2=$G^{(2)}_{\mathrm{univ}}$}
{wiki}
= Countable random graph
{synonym}
The Rado graph is the unique countably infinite <graph> with the two-uniform <hypergraph extension property>. Equivalently, for any disjoint finite vertex sets $U,W$, some new vertex is adjacent to every member of $U$ and no member of $W$. The <back-and-forth method> proves uniqueness. Independent edge sampling on the <natural numbers> with any fixed $p\in(0,1)$ produces this graph <almost surely>. It contains both edges and nonedges and therefore is not a <complete graph>. Its first-order axioms constitute the <theory of the random graph>.
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