C*-equivalences of graphs

Several relations on graphs, including primitive equivalence, explosion equivalence and strong shift equivalence, are examined and shown to preserve either the graph groupoid, a construction of Kumjian, Pask, Raeburn, and Renault, or the groupoid of a pointed version of the graph. Thus these relations preserve either the isomorphism class or the Morita equivalence class of the graph C*-algebra, as defined by Kumjian, Pask, and Raeburn.