The hidden simplicity of metabolic networks is revealed by multireaction dependencies.

Understanding the complexity of metabolic networks has implications for manipulation of their functions. The complexity of metabolic networks can be characterized by identifying multireaction dependencies that are challenging to determine due to the sheer number of combinations to consider. Here, we propose the concept of concordant complexes that captures multireaction dependencies and can be efficiently determined from the algebraic structure and operational constraints of metabolic networks. The concordant complexes imply the existence of concordance modules based on which the apparent complexity of 12 metabolic networks of organisms from all kingdoms of life can be reduced by at least 78%. A comparative analysis against an ensemble of randomized metabolic networks shows that the metabolic network of contains fewer concordance modules and is, therefore, more tightly coordinated than expected by chance. Together, our findings demonstrate that metabolic networks are considerably simpler than what can be perceived from their structure alone.