Shape Indexes of Orders One and Three from Molecular Graphs

Abstract The concept of a shape index derived from the molecular graph previously described, has been expanded to include two additional indexes derived from counts of one‐path and three‐path fragments. Algorithms have been derived using the original model of defining two limiting structures and quantitating any intermediate structural shape relative to these two. Counts of one‐path fragments and three‐path fragments lead to shape indexes of 1 K and 3 K. The information encoded in each has been extracted in terms of shape attributes. The concept that molecular shape can be viewed as a sum of isolated attributes is put forward and a partial series is presented based on the indexes developed to date. Several examples of QSAR applications are presented where two of these shape indexes are revealed to encode enough information to give good correlations.