A D778: Graph $G = (X, \mathcal{E})$ is complete if and only if \begin{equation} \mathcal{E} = \mathcal{P}_2(X) \end{equation}

A D778: Graph $G = (X, \mathcal{E})$ is complete if and only if \begin{equation} \forall \, x, y \in X \, (x \neq y \quad \implies \quad \{ x, y \} \in \mathcal{E}) \end{equation}