Definition: A Subgraph S of a graph G is a graph whose vertex set V(S) is a subset of the vertex set V(G), that is V(S)⊆V(G), and whose edge set E(S) is a subset of the edge set E(G), that is E(S)⊆E(G).

Essentially, a subgraph is a graph within a larger graph. For example, the following graph S is a subgraph of G:

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