Let $G_X = (X, \mathcal{E}_X)$ be a D778: Graph.
An D548: Ordered pair $G_Y = (Y, \mathcal{E}_Y)$ is a complement of $G_X$ if and only if

(1)	$X = Y$
(2)	$\mathcal{E}_Y = \mathcal{P}_2(X) \setminus \mathcal{E}_X$