Weakly reversible deficiency zero realizations of reaction networks

Abstract

We prove that if a given reaction network $\mathcal{N}$ has a weakly reversible deficiency zero realization for all choice of rate constants, then there exists a $\text{unique}$ weakly reversible deficiency zero network ${\mathcal{N}}^{\prime }$ such that $\mathcal{N}$ is realizable by ${\mathcal{N}}^{\prime }$. Additionally, we propose an algorithm to find this weakly reversible deficiency zero network ${\mathcal{N}}^{\prime }$ when it exists.

21 pages, 3 figures