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A [[multigraph]] is a generalization that allows multiple edges to have the same pair of endpoints. In some texts, multigraphs are simply called graphs.{{sfn|Bender|Williamson|2010|p=149}}<ref>Graham et al., p. 5.</ref>
Sometimes, graphs are allowed to contain ''[[Loop (graph theory)|loop]]s'', which are edges that join a vertex to itself. To allow loops, the pairs of vertices in {{mvar|E}} must be allowed to have the same node twice. Such generalized graphs are simply called ''graphs with loops'' or
Generally, the vertex set {{mvar|V}} is taken to be finite (which implies that the edge set {{mvar|E}} is also finite). Sometimes [[infinite graph]]s are considered, but they are usually viewed as a special kind of [[binary relation]], because most results on finite graphs either do not extend to the infinite case or need a rather different proof.
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