Figure 2

Reactions, hyperpath, and corresponding stoichiometric matrix. A) A set of reactions (top), the corresponding hypergraph, and the corresponding stoichiometric matrix (bottom). The hypergraph here represented is a hyperpath from v₂ and v₄ (source nodes) to the target vertex v₈. The reactions can be ordered R₃, R₂, R₁ so that the conditions required by the hyperpath definition (3) are satisfied; B. A hypergraph that is not a hyperpath: The hypergraph {R₁, R₂} is not a hyperpath with source a; C) A minimal hyperpath: This hyperpath is a subset of the hyperpath in Figure 2A and is minimal (both R₁ and R₃ are necessary to link v₈ to the source); D) A hypergraph representing a toy metabolic network: Given v₁ and v₄ as sources of the hypergraph above the reachable vertices are v₅, v₇, v₈, v₉, v₁₂ in light green. v₂ and v₃ are bootstrap compounds: the presence of one of them permits its own production. In red the compounds v₁₀ and v₁₁ are supplements for the production of v₂, v₃, v₆ and v₈.