  We investigate the expected value of various graph parameters associated with
the minimum rank of a graph, including minimum rank/maximum nullity and related
Colin de Verdi\`ere-type parameters. Let $G(v,p)$ denote the usual
Erd\H{o}s-R\'enyi random graph on $v$ vertices with edge probability $p$. We
obtain bounds for the expected value of the random variables ${\rm
mr}(G(v,p))$, ${\rm M}(G(v,p))$, $\nu(G(v,p))$ and $\xi(G(v,p))$, which yield
bounds on the average values of these parameters over all labeled graphs of
order $v$.

Combinatorics