Efficient computation of impact degrees for multiple reactions in metabolic networks with cycles

Analysis of the robustness of a metabolic network against of single or multiple reaction(s) is useful for mining important enzymes/genes. For that purpose, the impact degree was proposed by Jiang et al. In this short paper, we extend the impact degree for metabolic networks containing cycles and develop a simple algorithm for its computation. Furthermore, we propose an improved algorithm for computing impact degrees for deletions of multiple reactions. The results of preliminary computational experiments suggest that the improved algorithm is several tens of times faster than a simple algorithm.