Terminology for a graph obtained from another by adding edges

$H$ is a supergraph of $G$ if it can be obtained from $G$ by adding, edges, vertices, or both.

Is there a standard terminology for a graph that can be obtained from $G$ only by adding edges?

If $H$ is made by adding only edges to $G$, then $G$ is a spanning subgraph of $H$. However, I'm not aware of any way of phrasing it that makes $H$ the subject of the sentence.

StackExchange Computer Science Q#60284, answer score: 3