  Our approach to structural matrix rings defines them over preordered directed
graphs. A grading of a structural matrix ring is called a good grading if its
standard unit matrices are homogeneous. For a group $G$, a $G$ -grading set is
a set of arrows with the property that any assignment of these arrows to
elements of $G$ uniquely determines an induced good grading. One of our main
results is that a $G$-grading set exists for any transitive directed graph if
$G$ is a group of prime order. This extends a result of Kelarev. However, an
example of Molli Jones shows there are directed graphs which do not have
$G$-grading sets for any cyclic group $G$ of even order greater than 2.
Finally, we count the number of nonequivalent elementary gradings by a finite
group of a full matrix ring over an arbitrary field.
