A New Algorithm for Exhaustive Ring Perception in a Molecular Graph

A new fast and easy to implement algorithm for exhaustive ring perception is presented. This algorithm is based upon a progressive reduction (collapsing) of the path graph associated with the molecular graph studied. The path graph is an image of the molecular graph in which each vertex corresponds to a vertex of the molecular graph and each edge a-b describes an existing path between a and b in the molecular graph. During the reduction, nodes of the path graph are removed, and the information related to cycle occurrence is concentrated in the label of new edges between the remaining vertices. Each loop formed in the path graph during this collapsing process corresponds to a cycle in the molecular graph. Once the path graph has totally collapsed, all the rings in the molecular graph have been perceived.