Definition:Subgraph

Definition
A graph $H = \struct {\map V H, \map E H}$ is called a subgraph of a graph $G = \struct {\map V G, \map E G}$ $\map V H \subseteq \map V G$ and $\map E H \subseteq \map E G$.

That is to say, it contains no vertices or edges that are not in the original graph.

If $H$ is a subgraph of $G$, then:
 * $G$ contains $H$
 * $H$ is contained in $G$.