An oriented simple graph is a graph with at most edge between each pair of vertices and where each edge has an orientation. Equivalently, it is a directed graph with at most one edge (of either orientation) between each pair of vertices. In contrast, the definition of a simple directed graph appears to allow at most one of each orientation.
Is isomorphism testing for oriented simple graphs GI-hard? Is there any discussion of the problem in the literature (perhaps using a different name for this class of graphs)?
A tournament has exactly one edge (of either orientation); isomorphism testing for tournaments appears to be open, but has at least been studied [1].
[1] https://link.springer.com/chapter/10.1007/978-3-540-74456-6_51
