Let $G_X = (X, \mathcal{E}_X)$ be a D778: Graph.
The set of subgraphs of $G_X$ is the D11: Set \begin{equation} \{ G_E = (E, \mathcal{E}_E) : E \subseteq X \text{ and } \mathcal{E}_E \subseteq \mathcal{E}_X \} \end{equation}