  We consider graphs E which have been obtained by adding one or more sinks to
a fixed directed graph G. We classify the C*-algebra of E up to a very strong
equivalence relation, which insists, loosely speaking, that C*(G) is kept
fixed. The main invariants are vectors W_E : G^0 -> N which describe how the
sinks are attached to G; more precisely, the invariants are the classes of the
W_E in the cokernel of the map A-I, where A is the adjacency matrix of the
graph G.
