The utility of the new reaction route (RR) graph theory developed in the preceding paper (Part 1) is illustrated here, with the help of two examples. In the first example, the kinetics of the conversion of 7,8-dihydrofolate and NADPH to 5,6,7,8-tetrahydrofolate and NADP, as catalyzed by dihydrofolate reductase (DHFR), is considered. This system is described by a linear kinetic mechanism that includes 13 elementary reaction steps. The second example is a microkinetic model of the water-gas shift reaction on a copper catalyst, which is highly nonlinear and includes 15 elementary surface reaction steps. For both mechanisms, the RR graphs have been constructed and used to determine the overall rates. The RR graphs and the overall rate equations are further simplified and reduced, using the RR network approach.