Search for isotypism in crystal structures by means of the graph theory

A method for the classification of crystal structures of chemical compounds is proposed, which is based on the representation of the system of interatomic bonds in a crystal as a finite 'reduced' graph. The program IsoTest is described, allowing one to find automatically the topological similarity (isotypism) for large groups of stoichiometrically and structurally different compounds. The analysis of crystal structures of simple and double sulfates and binary inorganic compounds was carried out and numerous examples of topological isotypism of the representatives of these groups of substances were found. It is shown that in many cases the ionic sublattices, constructed according to one of the close packings, can be selected in the sulfate crystal structures.