Within this application of the Polytope Formalism, graphs are used to describe and encode the relationships between the different atom-connectivity configurations. This graphical information describes the desmotropic transformation of one atom-connectivity configuration species into anotheror in the language of chemistrythis type of graph describes the concerted reaction pathways between the chemical species. The wider utility of using graphs arises from the suite of theorems and powerful tools that Graph Theory provides for processing graphs, determining their properties, and extracting information.