  Let $G$ be an undirected graph with $m$ edges and $d$ vertices. We show that
$d$-dimensional Ising models on $G$ can be learned from $n$ i.i.d. samples
within expected total variation distance some constant factor of $\min\{1,
\sqrt{(m + d)/n}\}$, and that this rate is optimal. We show that the same rate
holds for the class of $d$-dimensional multivariate normal undirected graphical
models with respect to $G$. We also identify the optimal rate of $\min\{1,
\sqrt{m/n}\}$ for Ising models with no external magnetic field.
