  Wildberger has introduced the method to construct a hermitian discrete
hypergroup from a random walk on a graph. We will apply his method to an open
quantum random walk (OQRW) on a distance set, and show that any discrete
hypergroup which is not necessary hermitian is realized by an OQRW on a
distance set. We will investigate distributions of OQRWs on distance sets in
the view point of hypergroups.
