Let $G( n, m )$ be the set of all possible connected graphs of $n$ nodes and $m$ edges such that, for each $g_1 \in G( n, m )$, $g_2 \in G( n, m )$, if $g_1 \neq g_2$ then $g_1$ and $g_2$ are non-isomorphic.
Question
How large can $|G( n, m )|$ be? Is it polynomial in both $n$ and $m$? Or is it superpolynomial in either $n$ or $m$?