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Is there a name for graphs which contain oriented and non-oriented edges?

I couldn't find on the internet if there exist a specific name for such graphs.

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They are called mixed graphs.

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Yes. ​ (Nothing stops them from having both $\langle u,v\rangle$ and $\langle v,u\rangle$ as edges.)

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  • $\begingroup$ Ricky means that the usual convention is to think of undirected graphs as directed graphs in which each undirected edge $\{u,v\}$ corresponds to two directed edges $\langle u,v \rangle, \langle v,u \rangle$, and you can use this correspondence for mixed graphs as well. $\endgroup$ Apr 28, 2016 at 9:27

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