The routing problem in networks is solved by either maintaining at every node detailed routing information for all destinations (explicit routing) or by exploiting the information implicit in an a-priori labelling of nodes and links (implicit routing). Efficient implicit routing algorithms are known only for networks modelled by graphs having special topologies (e.g. ring, hypercube). In this paper, a labelling scheme for graphs of arbitrary topology is presented, and an implicit routing algorithm is derived. The proposed algorithm is shown to be optimal for acyclic graphs, and to exhibit a worst-case complexity which is within a factor of two from the optimal solution for graphs of arbitrary topology. Limitations to the applicability of the proposed solutions to communication networks are discussed.