Inclusion of Symmetry as a Shape Attribute in Kappa Index Analysis

The molecular shape attribute of symmetry is introduced as a supplement to the shape attributes encoded by the kappa values. This attribute is indexed by the Shannon equation for information content and is designated as 0 κ within the framework of multiple path, path and atom counts to derive the kappa values. A new procedure is introduced to calculate a label characterizing the uniqueness or equivalence of atoms in a molecule using the connection matrix. This label, called the relative topological state, is used in the Shannon equation to calculate the information content or 0 κ. Two examples illustrate the utility of 0 κ along with other kappa values to encode attributes of molecular shape influencing physical and biological properties.