Relevant Cycles in Chemical Reaction Networks

We characterize the distributions of short cycles in a large metabolic network previously shown to have small world characteristics and a power law degree distribution. Compared with three classes of random networks, including Erdős–Renyi random graphs and synthetic small world networks of the same connectivity, both the metabolic network and models for the chemical reaction networks of planetary atmospheres have a particularly large number of triangles and a deficit in large cycles. Short cycles reduce the length of detours when a connection is clipped, so we propose that long cycles in metabolism may have been selected against in order to shorten transition times and reduce the likelihood of oscillations in response to external perturbations.