Ordered cyclic motifs contribute to dynamic stability in biological and engineered networks

Proc Natl Acad Sci U S A. 2008 Dec 9;105(49):19235-40. doi: 10.1073/pnas.0805344105. Epub 2008 Nov 25.


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.

Publication types

  • Research Support, N.I.H., Extramural

MeSH terms

  • Animals
  • Aviation
  • Biophysics / methods*
  • Brain Mapping
  • Caenorhabditis elegans / physiology
  • Computer Simulation*
  • Ecology
  • Engineering / methods
  • Escherichia coli / physiology
  • Feedback, Physiological
  • Ferric Compounds
  • Food Chain
  • Gene Regulatory Networks
  • Internet
  • Models, Biological*
  • Saccharomyces cerevisiae / physiology
  • Signal Transduction


  • Ferric Compounds
  • ferrite