In reaction network theory, the Volpert graph plays a very important role. As an abstract idea of reaction kinetics, it is a directed bipartite graph. The vertex set contains the chemical components and the reaction steps, which are the two disjoint classes of the graph. There is an edge between a component and a reaction if and only if the reactant complex contains the component; otherwise, there is an edge between a reaction and a component if and only if the product complex contains the component.
The Volpert graph of the formal reaction mechanism is the following directed bipartite graph: , where the vertex set is the set , and iff , and iff , where and . There is no directed edge inside nor .
For more information about the formal reaction mechanism see the "Descriptive Reaction Kinetics" Demonstration.
P. Érdi and J. Tóth, Mathematical Models of Chemical Reactions: Theory and Applications of Deterministic and Stochastic Models, Manchester: Manchester University Press, 1989.