Given the reaction graph for some chemical system, the principles of transition-state theory (TST) can be applied by associating the relative energies, energy gradients, and curvatures for the component species with their respective graph vertices. This facilitates an encoding of the essential features of a PES; this is what is meant by the reaction graph describing the associated chemical space. Further, this reaction-graph -PES relationship is a feature of the Polytope Formalism where graphs of the same topology can describe the idiosyncrasies of PESs for different chemical systems.