A subgraph 
of a graph 
is a graph 
whose vertex set and edge
set are subsets of those of 
. If 
is a subgraph of 
,
then 
is said to be a supergraph
of 
(Harary 1994, p. 11).
A vertex-induced subgraph, often simply called "an induced subgraph" (e.g., Harary 1994, p. 11) of 
induced by the vertex set 
(where 
is a subset of the vertex set
of 
) is the graph 
with vertex set 
and edge set consisting of those
edges both of whose endpoints are in 
.
