ABSTRACT
Program for Theory of Complex Systems, Texas A&M University,
Galveston, Texas, 77553-1675, USA, and
Assen Zlatarov University, Burgas 8010, Bulgaria
Molecular complexity concepts and related quantitative molecular descriptors are outlined. The recent concept which specifies topological complexity as overall connectivity, and generalizes the idea of molecular connectivities of Randie, Kier, and Hall, is presented in more detail. Two overall connectivity indices, TC and TCI, are defined as the connectivity (the sum of the vertex degrees) of all connected subgraphs in the molecular graph. The contributions to TC and TCI, that originate from all subgraphs having the same number of edges e, form two sets of eth order overall connectivities, eTC and eTCI. The total number of subgraphs K, introduced by Gordon and Kennedy, is also shown to be useful as complexity measure, and the vector of its eth order components, e K, is examined as well. The K, TC, and TCI indices match very well the increase in molecular complexity with the increase in the number of atoms and, at a constant number of atoms, with the increased degree of branching and cyclicity of molecular skeleton. The three sets of eth order complexities outperform the molecular connectivities kX of Kier and Hall, as demonstrated in a series of QSPRs with alkane properties (heats of formation, heats of vaporization, heats of atomization, boiling points, critical temperature, critical pressure, molar volume, molecular refraction, and surface tension). A forthcoming paper extends the application of the overall connectivity concept to QSAR studies.
