A strong connectivity decomposition method for analyzing the multi-equilibrium property of metabolic networks with no inhibition

For metabolic networks without inhibition, a strong connectivity decomposition (SCD) method is proposed, which can not only divide the whole network into a set of sub-networks but also keep the strong connectivity of the network. This makes it possible to understand the multi-equilibrium property of the whole network by analyzing the sub-networks. The SCD method is based on only the topological structure of the network. To get an SCD for a given metabolic network, the concepts of metabolic reaction graph, interaction graph and contraction operation are introduced. It is shown that for a given metabolic network, the SCD is unique, all the sub-networks are strongly connected, and the computational complexity of the decomposition is polynomial. The relationship between the whole network and sub-networks is given in the sense of multi-equilibrium properties. Examples are given to demonstrate the effectiveness of the algorithms and the main results.