A
graph
is a non-empty finite set V of elements called
vertices
together with a possibly empty set E of pairs of vertices
called
edges.
Here are a few examples of graphs:

Vertex set V={a, b, c, d} and edge set E={(a, b), (b, d)}

Vertex set V={1, 2, 3, 4} and edge set E={(2, 4)}

Vertex set V={wolf, goat, cabbage} and edge set
E={(wolf, cabbage)}