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Previous studies of properties of metabolic works have mainly focused on the statistic properties of networks, including the small world, and power-law distribution of node degree, and building block of network motifs. Symmetry in the metabolic networks has not been systematically investigated. In this report, symmetry in directed graph was introduced and an algorithm to calculate symmetry in directed and disconnected graphs was developed. We calculated several indices to measure the degree of symmetry and compared them with random networks. We showed that metabolic networks in KEGG and BioCyc databases are generally symmetric and in particular locally symmetric. We found that symmetry in metabolic networks is distinctly higher than that in random networks. We obtained all the orbits in networks which are defined as structurally equivalent nodes and found that compound pairs in the same orbit show much more similarity in chemical structures and function than random compound pairs in network, which suggests that symmetry in the metabolic network can generate the functional redundancy, increase the robustness and play an important role in network structure, function and evolution.
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