Pathway Length and Reaction Participation Matrices for a simple network. (A) The example system with its corresponding stoichiometric and extreme pathway matrix. (A,bottom) Corresponding maps of the three extreme pathways. (B,C) The corresponding Length and Participation Matrices, as well as their respective properties. Note in Athat although the metabolite byp only participates in one exchange flux, b3, there are two exchange flux arrows in the figure. However, both arrows correspond to the same single exchange flux.