A Schurian coherent configuration is a coherent configuration whose relations are the orbitals of
a permutation group acting on the underlying
set. Equivalently, its relations are exactly the orbits of the componentwise action
of the group on ordered pairs of elements.
The orbital coherent configuration of a permutation group is homogeneous if and only if that group is transitive. In this case, the configuration is a Schurian
scheme.
