# Is there a term for a subgraph which includes all the edges of a graph?

A subgraph is called spanning when it includes all of the vertices of the given graph.

Is there a term for a subgraph which includes all the edges of a graph?

Thanks.

If the subgraph includes all edges of the original graph, then it also includes all its vertices, except maybe some with degree $$0$$.
The minimal such subgraph is the graph in which all $$0$$-degree vertices were removed. It is called the $$1$$-core of the graph, a very special case of $$k$$-core.