A reaction network is a finite directed graph whose vertices, called complexes, are multisets of 
species, represented by vectors
in 
, and whose directed edges
are reactions 
(Boros and Hofbauer 2020). The nonnegative integer coordinates of a complex give its species multiplicities.
For example, 
is the complex 
in a two-species network. Each reaction determines the vector 
, and their vector
space span is the stoichiometric subspace.
Assigning positive rate constants and using the monomials 
yields a mass-action
system (Gunawardena 2003, pp. 3-5). A weakly
reversible reaction network has a directed graph path
from 
back to 
for every reaction 
.
Reaction Network
See also
Directed Graph, Mass-Action System, Multiset, Stoichiometric Subspace, Weakly Reversible Reaction NetworkExplore with Wolfram|Alpha
References
Boros, B. and Hofbauer, J. "Permanence of Weakly Reversible Mass-Action Systems with a Single Linkage Class." SIAM J. Appl. Dyn. Syst. 19, 352-365, 2020. https://doi.org/10.1137/19M1248431.Gunawardena, J. "Chemical Reaction Network Theory for In-Silico Biologists." 20 Jun 2003. https://vcp.upf.edu/papers/crnt.pdf.Cite this as:
Weisstein, Eric W. "Reaction Network." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ReactionNetwork.html