  The characterization of the notions of complex and detailed balancing for
mass action kinetics chemical reaction networks is revisited from the
perspective of algebraic graph theory, in particular Kirchhoff's Matrix Tree
theorem for directed weighted graphs. This yields an elucidation of previously
obtained results, in particular with respect to the Wegscheider conditions, and
a new necessary and sufficient condition for complex balancing, which can be
verified constructively.
