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==Formal definition== Given a graph {{mvar|G}}, its line graph {{math|''L''(''G'')}} is a graph such that * each [[vertex (graph theory)|vertex]] of {{math|''L''(''G'')}} represents an edge of {{mvar|G}}; and * two vertices of {{math|''L''(''G'')}} are [[Adjacent (graph theory)|adjacent]] if and only if their corresponding edges share a common endpoint ("are incident") in {{mvar|G}}. That is, it is the [[intersection graph]] of the edges of {{mvar|G}}, representing each edge by the set of its two endpoints.<ref name="h72-71"/>
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