  We describe proper correspondences from graph C*-algebras to arbitrary
C*-algebras by K-theoretic data. If the target C*-algebra is a graph C*-algebra
as well, we may lift an isomorphism on a certain invariant to correspondences
back and forth that are inverse to each other up to ideal-preserving homotopy.
This implies a classification theorem for purely infinite graph C*-algebras up
to stable isomorphism.
