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.