  We show that if the degree sequence of a graph $G$ is close in
$\ell_1$-distance to a given realizable degree sequence $(d_1,\dots,d_n)$, then
$G$ is close in edit distance to a graph with degree sequence
$(d_1,\dots,d_n)$. We then use this result to prove that every graph property
defined in terms of the degree sequence is testable in the dense graph model
with query complexity independent of $n$.
