Model reduction of detailed-balanced reaction networks by clustering linkage classes

We propose a model reduction method that involves sequential application of clustering of linkage classes and Kron reduction. This approach is specifically useful for chemical reaction networks with each linkage class having less number of reactions. In case of detailed balanced chemical reaction networks that are governed by general enzyme kinetics, we show that our procedure ensures that the space of equilibria corresponding to the original model is a subspace of the space of equilibria of the reduced model