  A mixed graph is cospectral to its converse, with respect to the usual
adjacency matrices. Hence, it is easy to see that a mixed graph whose
eigenvalues occur uniquely, up to isomorphism, must be isomorphic to its
converse. It is therefore natural to ask whether or not this is a common
phenomenon. This note contains the theoretical evidence to confirm that the
fraction of self-converse mixed graphs tends to zero.
