Parametric uniqueness of deficiency zero reaction networks

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In this paper it is shown that deficiency zero mass action reaction networks containing one terminal linkage class are parametrically and therefore structurally unique with a fixed complex set. Clearly, weakly reversible deficiency zero networks with one linkage class belong to this class. However, it is shown through an illustrative example that deficiency zero networks with several linkage classes can have multiple dynamically equivalent realizations, even if the individual linkage classes are weakly reversible.