Graphical matrices in chemistry

Graphical matrices are presented. Their construction via selected sets of subgraphs and the replacement of subgraphs by numbers representing graph invariants are discussed. The last step of the procedure is applying the method of choice to obtain the desired double invariant from the graphical matrix in the numerical form. It is also pointed out that many so-called special graph-theoretical matrices from the literature are rooted in the corresponding graphical matrices. As examples of double invariants, two descriptors, the Wiener-Wiener index and the Hosoya-Wiener index, have been generated from the appropriate graphical matrices and used in the structure-boiling point and structure-steric energy modeling of octanes. The obtained models possess statistical parameters comparable to those of the best structure-boiling point and structure-steric energy models for octanes in the literature