A Shape Index from Zero-Order Paths

A Shape Index from Zero-Order Paths 

Based on path counts, it may be also possible to define a zeroth order index, °K. It follows from our path count development that k should be derived from °P fragments, a quantity that is, in fact, the count of atoms in a molecular graph. One attribute of an atom that should influence the shape of a molecule is the topological uniqueness of that atom within the molecule. One collective effect of atom topological uniqueness is the symmetry or redundancy of the molecule. 

Atom uniqueness or redundancy is certainly a shape attribute that must play some role in the influence of structure on function. One approach to the quantitation of uniqueness is the use of the Shannon equation for information content,which has been studied quite thoroughly by Brillouin and Bon-chev. Kier has made use of the equation to encode molecular uniqueness, or negentropy, and to relate to biological and physical properties. 

Two interrelated values may be derived from the Shannon equation. The first of these is 1, the information content per atom  

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