Contractible subgraphs and Morita equivalence of graph C-algebras

Proc. Amer. Math. Soc. 134 (2006), no. 7, 2003-2013 In this paper we describe an operation on directed graphs which produces a graph with fewer vertices, such that the C*-algebra of the new graph is Morita equivalent to that of the original graph. We unify and generalize several related constructions, notably delays and desingularizations of directed graphs.