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}}. [http://diestel-graph-theory.com/index.html Electronic edition], page 4.</ref>
For [[directed graph]]s, the complement can be defined in the same way, as a directed graph on the same vertex set, using the set
The complement is not defined for [[multigraph]]s. In graphs that allow [[loop (graph theory)|self-loops]] (but not multiple adjacencies) the complement of {{mvar|G}} may be defined by adding a self-loop to every vertex that does not have one in {{mvar|G}}, and otherwise using the same formula as above. This operation is, however, different from the one for simple graphs, since applying it to a graph with no self-loops would result in a graph with self-loops on all vertices.
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