Kinetic modeling is increasingly used to understand the reaction dynamics of metabolic systems. However, one major drawback of kinetic modeling is that appropriate rate parameters required to implement such models are often unavailable. To circumvent this limitation, an approach known as structural kinetic modeling was developed as a way to understand the dynamics of reaction networks without explicitly requiring rate parameters. This study describes a novel approach to use structural kinetic modeling to identify reaction components that contribute most significantly to mediating network stability. We applied this method to analyze the metabolic pathway of glycolysis in yeast. As a result, we identified specific metabolic components that contribute most significantly to defining the stability properties of the glycolysis reaction network and predict the responses of these components to perturbations. These results were validated via comparison to a conventional kinetic model of glycolysis. Thus, applying our approach allows more detailed information about the stability and dynamics of the metabolic network to now be accessible without requiring rate parameters. We anticipate that this method can focus efforts of experimental studies by identifying the susceptibility of reaction components to metabolic engineering. The approach may be applied to a variety of complex reaction networks.