In reaction network theory, the Feinberg–Horn–Jackson graph plays a very important role. Reaction kinetics can be viewed abstractly as a directed graph in which the vertex set contains the complexes; there is an edge between two complexes if and only if there is a reaction step between them.

By a complex chemical reaction we mean a set of reaction steps , where are chemical species (molecules, radicals, ions, etc.), the non-negative integers and are the stoichiometric coefficients or molecularities, and the formal linear combinations and are the reactant and product complexes, respectively.

The Feinberg–Horn–Jackson graph of a complex chemical reaction is the directed graph , where the vertex set is the set of different reaction complexes and the arrows are the reaction steps.

[1] P. Érdi and J. Tóth, Mathematical Models of Chemical Reactions: Theory and Applications of Deterministic and Stochastic Models, Manchester: Manchester University Press, 1989.