The concepts of chain graph, general graph, and complete graph have been used to implement the graph framework of molecular connectivity (MC) theory. Some concepts of this theory have been addressed using ''external'' theoretical concepts belonging mostly to quantum or structural chemistry, with no direct counterpart in graph theory. Thus, while the concept of chain graph can be used to tackle the cis-trans isomerism problem, the concept of pseudograph, or general graph can be used to tackle the description of the sigma-, pi-, and nonbonding n-electrons. The concept of complete graph can instead be used to tackle the electron core problem of the atoms of a molecule. Graph concepts can also be used to tackle the problem of the hydrogen contribution in hydrogen depleted graphs, which are encoded by the aid of a perturbation parameter, which differentiates between compounds with similar hydrogen-suppressed chemical graphs, like the graphs of CH 3 F and BH 2 F. These concepts have allowed redesign of a central parameter of MC theory, the valence delta, giving MC indices with improved model quality as exemplified here with different properties for each treated topic. ร 2007