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Is there a name for a kind of graph where edges are vertices in the same graph ?

A example would be :

e1(a,b) e2(c,d) e3(e1,e)

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    This could pretty much be interpreted as the hypergraph with edges $\{c,d\}$ and $\{a,b,e\}$ if that is what you want.2012-10-10

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