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