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