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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 propertydefined in terms of the degree sequence is testable in the dense graph modelwith query complexity independent of $n$.

Modifying a Graph's Degree Sequence and the Testablity of Degree Sequence Properties