Graphical matrices are matrices whose elements are subgraphs of the graph rather than numbers. Since the elements of these matrices are (sub)graphs, they are called the graphical matrices [357]. Thus far limited work has been reported on these matrices [357-360]. However, many of so-called special matrices presented above, such as the Wiener matrices and the Hosoya matrices, may be regarded as the numerical realizations of the corresponding graphical matrices. The advantage of graphical matrices lies in the fact that they allow many possibilities of numerical realizations. In order to obtain a numerical form of a graphical matrix, one needs to select a graph invariant and replace all the graphical elements (subgraphs of some form) by the corresponding numerical values of the selected invariant. In this way, the numerical form of the graphical matrix is established and one can select another or the same type of invariant - this time an invariant of the numerical matrix. Graph invariants generated in this way are double invariants in view of the fact that two invariants are used in constructing a given molecular descriptor.
1. Construction of Graphical Matrices
2. Numerical Realization of Graphical Matrices
2.1. Use of the Randic Connectivity index
2.2. Use of the Hosoya Index
3. Generalized Method for Constructing Graphical Matrices and for Getting Their Numerical Representations