“…After a brief review of the established definitions and notations for graph algebras, we state and prove our main result, Theorem 3.1, which shows that any finite tree is contractible in the above sense, and that a similar construction may be applied to more general acyclic subgraphs. In particular, this theorem combines several of the separate results of [4] and may cover some further examples as well. Our proof follows closely the direct methods of [4], and makes use of a powerful theorem of [3], the gauge-invariant uniqueness theorem.…”