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In this paper we derive a compact mathematical formulation describing thedynamics of chemical reaction networks that are complex-balanced and aregoverned by mass action kinetics. The formulation is based on the graph of(substrate and product) complexes and the stoichiometric information of thesecomplexes, and crucially uses a balanced weighted Laplacian matrix. It is shownthat this formulation leads to elegant methods for characterizing the space ofall equilibria for complex-balanced networks and for deriving stabilityproperties of such networks. We propose a method for model reduction ofcomplex-balanced networks, which is similar to the Kron reduction method forelectrical networks and involves the computation of Schur complements of thebalanced weighted Laplacian matrix.

A Graph-Theoretical Approach for the Analysis and Model Reduction of Complex-Balanced Chemical Reaction Networks