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 .