Relationship between extreme pathways and structurally minimal pathways

The determination of reaction pathways is one of the most important functions that should be performed in exploring the kinetics of catalyzed chemical reactions or biochemical reactions, the latter being generally catalyzed by enzymes. It is proven that the terms, "type-I extreme pathway" and "structurally minimal pathway", both introduced to characterize the kinetics of a catalyzed reaction are equivalent. These two terms are based on two distinct methodologies, one mainly rooted in convex analysis and the other in graph theory. The equivalence promises further even more effective methods for reaction-pathway identification by synergistic integration of existing ones.