The concept of computer generated reaction modelling was broadened through the development of a general planar graph algorithm for determination of isomorphism. The previous capability was limited by its inability to determine the uniqueness of ring-containing species unambiguously, restricting the application of automatic network generation to non-cyclic species or cyclic species where the ring was not involved in the chemical transformation. In this work, the systematic identification of both noncyclic and cyclic species was carried out by constructing the structurally explicit decomposition tree, an assembly of the biconnected components of the graph, from which a graph invariant unique string code was obtained by iteratively encoding and ordering the subtrees of the decomposition tree. A lexicographical comparison of the unique string code of the candidate species with the string codes of all previously generated species with the same empirical formula allowed unambiguous determination of species uniqueness.