  Seymour's Second Neighborhood Conjecture (SNC) states that every oriented
graph contains a vertex whose second neighborhood is as large as its first
neighborhood. We investigate the SNC for orientations of both binomial and
pseudo random graphs, verifying the SNC asymptotically almost surely (a.a.s.)
  (i) for all orientations of $G(n,p)$ if $\limsup_{n\to\infty} p < 1/4$; and
  (ii) for a uniformly-random orientation of each weakly
$(p,A\sqrt{np})$-bijumbled graph of order $n$ and density $p$, where
$p=\Omega(n^{-1/2})$ and $1-p = \Omega(n^{-1/6})$ and $A>0$ is a universal
constant independent of both $n$ and $p$.
  We also show that a.a.s. the SNC holds for almost every orientation of
$G(n,p)$. More specifically, we prove that a.a.s.
  (iii) for all $\varepsilon > 0$ and $p=p(n)$ with $\limsup_{n\to\infty} p \le
2/3-\varepsilon$, every orientation of $G(n,p)$ with minimum outdegree
$\Omega_\varepsilon(\sqrt{n})$ satisfies the SNC; and
  (iv) for all $p=p(n)$, a random orientation of $G(n,p)$ satisfies the SNC.
