  We clarify that coined quantum walk is determined by only the choice of local
quantum coins. To do so, we characterize coined quantum walks on graph by
disjoint Euler circles with respect to symmetric arcs. In this paper, we
introduce a new class of coined quantum walk by a special choice of quantum
coins determined by corresponding quantum graph, called quantum graph walk. We
show that a stationary state of quantum graph walk describes the eigenfunction
of the quantum graph.
