  In this paper we derive a compact mathematical formulation describing the
dynamics of chemical reaction networks that are complex-balanced and are
governed by mass action kinetics. The formulation is based on the graph of
(substrate and product) complexes and the stoichiometric information of these
complexes, and crucially uses a balanced weighted Laplacian matrix. It is shown
that this formulation leads to elegant methods for characterizing the space of
all equilibria for complex-balanced networks and for deriving stability
properties of such networks. We propose a method for model reduction of
complex-balanced networks, which is similar to the Kron reduction method for
electrical networks and involves the computation of Schur complements of the
balanced weighted Laplacian matrix.
