  This paper presents novel decomposition classes of chemical reaction networks
(CRNs) derived from S-system kinetics. Based on the network decomposition
theory initiated by Feinberg in 1987, we introduce the concept of incidence
independent decompositions and develop the theory of $\mathscr{C}$- and
$\mathscr{C}^*$- decompositions which partition the set of complexes and the
set of nonzero complexes respectively, including their structure theorems in
terms of linkage classes. Analogous to Feinberg's independent decomposition, we
demonstrate the important relationship between sets of complex balance
equilibria for an incidence independent decomposition of weakly reversible
subnetworks for any kinetics. We show that the $\mathscr{C}^*$-decompositions
are also incidence independent. We also introduce in this paper a new
realization for an S-system that is analyzed using a newly defined class of
species coverable CRNs. This led to the extension of the deficiency formula and
characterization of fundamental decompositions of species decomposable reaction
networks.
