  We develop a model-independent reduction method of open chemical reaction
systems based on the stoichiometry, which determines their network topology. A
subnetwork can be eliminated systematically to give a reduced system with a
fewer number of degrees of freedom. The removal of the subnetwork is
accompanied by rewiring of the network, which is prescribed by the Schur
complement of the stoichiometric matrix. We introduce homology and cohomology
groups as a characterization of the topology of chemical reaction networks, and
the change of the topology under the reduction is traced by the changes of
those groups. We prove that, when certain topological conditions are met, the
steady-state chemical concentrations and reaction rates of the reduced system
is ensured to be the same as those of the original system. The result holds
regardless of the modeling of the reactions, namely chemical kinetics, since
the conditions involve topological information only. This is advantageous
because the details of reaction kinetics and parameter values are difficult to
identify in many practical situations. Our method can reduce a reaction network
while preserving its original steady-state properties, which allows us to study
large complex reaction systems efficiently. We demonstrate the reduction method
in hypothetical networks and the central carbon metabolism of Escherichia coli.
