In many applications, one is faced with the problem of identifying similar structural forms. This is usually performed in an intuitive manner and the outcome may be ambiguous. Here a well-defined approach for determining the degree of similarity among structures (molecular skeletons and more general graphs) is suggested. We select paths in a structure as the invariants upon which comparisons among structures should be based. For each structure, one first enumerates paths of different length and constructs a sequence of path numbers for the atoms (vertices). From such a list of atom codes, one can derive, by summing the contributions of individual atoms, a sequence of path numbers for a molecule (or a graph). The comparison of structures, thus, can be transformed into a comparison of sequences which are suitable for rigorous mathematical analysis. It is assumed that similar sequences imply similar structures, and, for selected examples, the validity of this assumption has been demonstrated. Molecules, generally considered similar, have been found to have similar sequences of path numbers, and molecules differing considerably in their connectivity show large differences in their path numbers. As an illustration of the concept of similarity based on path enumerations, we consider the problem of selecting from a set of structures those most similar to naturally occurring monocyclic monoterpenes. We used available computer-generated hypothetical monocyclic monoterpenes. The motive for this comparison is the assumption that potentially interesting skeletal forms should show considerable similarity to those found in natural structures. Such a technique may be of particular use in problems in chemical taxonomy. © 1979, American Chemical Society. All rights reserved.
