  As a generalization of the free semigroup algebras considered by Davidson and
Pitts, and others, the second author and D.W. Kribs initiated a study of
reflexive algebras associated with directed graphs. A free semigroupoid algebra
L_G is generated by a family of partial isometries, and initial projections,
acting on a generalized Fock space spawned from the directed graph G. We show
that if the graph is finite then the algebra L_G is hyper-reflexive.
