For a binary relation over a set, if each member in the set appears the same number of times in the first position and in the second position in the relation, is there a name for such a relation?
For example, in a $k$-regular directed graph, the in-degrees and the out-degrees of all the vertices are $k$. What it says is that in the edge set, each vertex appears $k$ times in the first position, and $k$ times in the second position.
Thanks.
These are graphs where the in-degree of each vertex is the same as its out-degree. These graphs receive the name of balanced.