  The one-way measurement model is a framework for universal quantum
computation, in which algorithms are partially described by a graph G of
entanglement relations on a collection of qubits. A sufficient condition for an
algorithm to perform a unitary embedding between two Hilbert spaces is for the
graph G, together with input/output vertices I, O \subset V(G), to have a flow
in the sense introduced by Danos and Kashefi [quant-ph/0506062]. For the
special case of |I| = |O|, using a graph-theoretic characterization, I show
that such flows are unique when they exist. This leads to an efficient
algorithm for finding flows, by a reduction to solved problems in graph theory.
