It is now possible to construct genome-scale metabolic networks for particular microorganisms. Extreme pathway analysis is a useful method for analyzing the phenotypic capabilities of these networks. Many extreme pathways are needed to fully describe the functional capabilities of genome-scale metabolic networks, and therefore, a need exists to develop methods to study these large sets of extreme pathways. Singular value decomposition (SVD) of matrices of extreme pathways was used to develop a conceptual framework for the interpretation of large sets of extreme pathways and the steady-state flux solution space they define. The key results of this study were: 1), convex steady-state solution cones describing the potential functions of biochemical networks can be studied using the modes generated by SVD; 2), Helicobacter pylori has a more rigid metabolic network (i.e., a lower dimensional solution space and a more dominant first singular value) than Haemophilus influenzae for the production of amino acids; and 3), SVD allows for direct comparison of different solution cones resulting from the production of different amino acids. SVD was used to identify key network branch points that may identify key control points for regulation. Therefore, SVD of matrices of extreme pathways has proved to be a useful method for analyzing the steady-state solution space of genome-scale metabolic networks.