Centric Index: Topological Shape
The centric index is a distance index, expressed as a value (number) that is reflecting the closeness of the vertices in the hypermolecule to the center of the hypermolecule’s network of vertices. It assesses the degree of compactness of the hypermolecule, showing a structure is more eccentric than others. The most known centric index is a Balaban centric index. To calculate this specific centric index, the vertices with a vertex degree of a unity are stepwise removed until no more vertices can be removed. The topological indices, however, can offer distance values for assessing branching, molecular size, shape, cyclicity, centricity, symmetry, etc. Correlations were made for alkanes having 4 to 8 carbon atoms in the molecule between their octane numbers and 14 topological descriptors. The Balaban Centric Index, especially the binormalized one, gave the best correlations with the octane numbers.