  The Rado Graph, sometimes also known as the (countable) Random Graph, can be
generated almost surely by putting an edge between any pair of vertices with
some fixed probability $p \in (0, 1)$, independently of other pairs. In this
article, we study the influence of allowing different probabilities for each
pair of vertices. More specifically, we characterize for which sequences
$(p_n)_{n\in \mathbb{N}}$ of values in $[0, 1]$ there exists a bijection f from
pairs of vertices in $\mathbb{N}$ to $\mathbb{N}$ such that if we put an edge
between $v$ and $w$ with probability $p_{f(\{v,w\})}$, independently of other
pairs, then the Random Graph arises almost surely.
