A direct relation graph with path flux analysis (DRGPFA) method for kinetic mechanism reduction has been proposed by Ju and coworkers [11]. Reduced mechanisms generated by the DRGPFA method have a comparable number of species as the DRG method while potentially being more accurate than that of either DRG or DRGEP over a varied range of conditions used for reduction.

With the error in the DRGEP method (Equation 3–21 ), also referred to as the direct interaction coefficient , only the first generation (directed relation) of the pre-selected species is considered. With path flux analysis, both the first generation and the second generation or the higher generations are important. Instead of using the absolute reaction rate, both the production and consumption fluxes are used to identify the important reaction pathways. The production and consumption fluxes, and , of species A are calculated as

(3–22)

(3–23)

And the flux of species A related to species B can be calculated as

(3–24)

(3–25)

Here and denote, respectively, the production and consumption rates of species A due to the existence of species B. The interaction coefficients for production and consumption of species A via B of the first generation are defined as

(3–26)

(3–27)

By using the production and consumption fluxes of the first generation, the interaction coefficients, which are the measures of flux ratios between A and B via a third reactant () for the second generation, are defined as

(3–28)

(3–29)

Finally, overall error is defined as

(3–30)

The coefficient defined in Equation 3–30 is used to evaluate the dependence of species B to species A in the mechanism.