%A Ma'ayan, Avi
%A Cecchi, Guillermo A.
%A Wagner, John
%A Rao, A. Ravi
%A Iyengar, Ravi
%A Stolovitzky, Gustavo
%T Ordered cyclic motifs contribute to dynamic stability in biological and engineered networks
%0 Journal Article
%D 2008
%8 December 9, 2008
%J Proceedings of the National Academy of Sciences
%P 19235-19240
%R 10.1073/pnas.0805344105
%V 105
%N 49
%U http://www.pnas.org/content/105/49/19235.abstract
%X Representation and analysis of complex biological and engineered systems as directed networks is useful for understanding their global structure/function organization. Enrichment of network motifs, which are over-represented subgraphs in real networks, can be used for topological analysis. Because counting network motifs is computationally expensive, only characterization of 3- to 5-node motifs has been previously reported. In this study we used a supercomputer to analyze cyclic motifs made of 3–20 nodes for 6 biological and 3 technological networks. Using tools from statistical physics, we developed a theoretical framework for characterizing the ensemble of cyclic motifs in real networks. We have identified a generic property of real complex networks, antiferromagnetic organization, which is characterized by minimal directional coherence of edges along cyclic subgraphs, such that consecutive links tend to have opposing direction. As a consequence, we find that the lack of directional coherence in cyclic motifs leads to depletion in feedback loops, where the number of nodes affected by feedback loops appears to be at a local minimum compared with surrogate shuffled networks. This topology provides more dynamic stability in large networks.