Figure 1: Illustration of the network concepts and the derived necessary condition for concentration robustness.

(a) Standard reaction diagram of a network in which six components, A–F, are interconverted by 10 reactions. The reaction diagram has n=8 nodes, corresponding to complexes and 10 edges, representing the reactions. The two linkage classes are surrounded by dashed lines. (b) Stoichiometric matrix N of the network in a. Reactions R₁, R₂ and R₃, with the corresponding edges in the reaction diagram and columns in N coloured in green, belong to the same linkage class (c) Standard reaction diagram for the network in a upon removal of component C. Since C exists as a single-component complex in a, its removal introduces the zero complex, O, coloured in green. This network contains n=7 nodes, 10 reactions, l=1 linkage class. (d) Standard reaction diagram for the network in a upon removal of component B. Since B exists as a single-component complex in a, its removal introduces the zero complex, 0, coloured in green. The network in a upon removal of B contains n=6 nodes, 10 reactions, l=1 linkage class. The structural deficiencies of the networks in a,b are δ_s=1, while for the network c, δ_s=0.