  The analysis of complex reaction networks is of great importance in several
chemical and biochemical fields (interstellar chemistry, prebiotic chemistry,
reaction mechanism, etc). In this article, we propose to simultaneously refine
and extend for general chemical reaction systems the formalism initially
introduced for the description of metabolic networks. The classical approaches
through the computation of the right null space leads to the decomposition of
the network into complex ``cycles'' of reactions concerned with all
metabolites. We show how, departing from the left null space computation, the
flux analysis can be decoupled into linear fluxes and single loops, allowing a
more refine qualitative analysis as a function of the antagonisms and
connections among these local fluxes. This analysis is made possible by the
decomposition of the molecules into elementary subunits, called "reactons" and
the consequent decomposition of the whole network into simple first order unary
partial reactions related with simple transfers of reactons from one molecule
to another. This article explains and justifies the algorithmic steps leading
to the total decomposition of the reaction network into its constitutive
elementary subpart.
