  Path sets are spaces of one-sided infinite symbol sequences associated to
pointed graphs (G_v_0), which are edge-labeled directed graphs G with a
distinguished vertex v_0. Such sets arise naturally as address labels in
geometric fractal constructions and in other contexts. The resulting set of
symbol sequences need not be closed under the one-sided shift. this paper
establishes basic properties of the structure and symbolic dynamics of path
sets, and shows they are a strict generalization of one-sided sofic shifts.
