# Feinberg-Horn-Jackson Graph

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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.

Contributed by: Attila Nagy (March 2009)

Open content licensed under CC BY-NC-SA

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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.

For more information see Chemical Reaction Network Theory.

Reference

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

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