Unique ring families: a chemically meaningful description of molecular ring topologies

The perception of a set of rings forms the basis for a number of chemoinformatics applications, e.g. the systematic naming of compounds, the calculation of molecular descriptors, the matching of SMARTS expressions, and the generation of atomic coordinates. We introduce the concept of unique ring families (URFs) as an extension of the concept of relevant cycles (RCs). URFs are consistent for different atom orders and represent an intuitive description of the rings of a molecular graph. Furthermore, in contrast to RCs, URFs are polynomial in number. We provide an algorithm to efficiently calculate URFs in polynomial time and demonstrate their suitability for real-time applications by providing computing time benchmarks for the PubChem Database. URFs combine three important properties of chemical ring descriptions, for the first time, namely being unique, chemically meaningful, and efficient to compute. Therefore, URFs are a valuable alternative to the commonly used concept of the smallest set of smallest rings (SSSR) and would be suited to become the standard measure for ring topologies of small molecules.