  We prove a $pre$-$asymptotic$ bound on the total variation distance between
the uniform distribution over two types of undirected graphs with $n$ nodes.
One distribution places a prescribed number of $k_T$ triangles and $k_S$ edges
not involved in a triangle independently and uniformly over all possibilities,
and the other is the uniform distribution over simple graphs with exactly $k_T$
triangles and $k_S$ edges not involved in a triangle. As a corollary, for $k_S
= o(n)$ and $k_T = o(n)$ as $n$ tends to infinity, the total variation distance
tends to $0$, at a rate that is given explicitly. Our main tool is Chen-Stein
Poisson approximation, hence our bounds are explicit for all finite values of
the parameters.
