We show that a number of conditions on oriented graphs, all of which are
satisfied with high probability by randomly oriented graphs, are equivalent.
These equivalences are similar to those given by Chung, Graham and Wilson in
the case of unoriented graphs, and by Chung and Graham in the case of
tournaments. Indeed, our main theorem extends to the case of a general
underlying graph G the main result of Chung and Graham which corresponds to the
case that G is complete.
One interesting aspect of these results is that exactly two of the four
orientations of a four-cycle can be used for a quasi-randomness condition,
i.e., if the number of appearances they make in D is close to the expected
number in a random orientation of the same underlying graph, then the same is
true for every small oriented graph HComment: 11 page