TBI-Preprint 00-10-058

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Small Cycles in Small Worlds

Petra M. Gleiss, Peter F. Stadler, Andreas Wagner, David A. Fell

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 Erdös-Rényi random graphs and synthetic small world networks of the same connectivity, the metabolic network has 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.

Keywords: Small World Networks, Metabolic Networks, Relevant Cycles
PACS Numbers 05.10.-a, 02.10.Eb, 87.58.-b

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