# What is a “mixed graph”?

I'm working on a digraph problem in which bidirectional edges need to be treated separately. As such, we could consider them as undirected edges. Clearly, if I replace bidirectional edges with undirected edges I get a mixed graph'' (one with directed and undirected edges). But can a mixed graph have bidirectional edges in addition to undirected edges? Can a mixed graph have a directed edge and an undirected edge between two vertices?

The Wikipedia definition is not crystal clear on this. A paper, Enumeration of Mixed Graphs indicates bidirectional and parallel mixed edges are disallowed. The definition in this article claims that the complete mixed graph'' has a undirected and bidirectional edge between both vertices.

What are mixed graphs'' typically defined as?

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