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An algorithm is given in this paper for the computation of dynamicallyequivalent weakly reversible realizations with the maximal number of reactions,for chemical reaction networks (CRNs) with mass action kinetics. The originalproblem statement can be traced back at least 30 years ago. The algorithm usesstandard linear and mixed integer linear programming, and it is based onelementary graph theory and important former results on the dense realizationsof CRNs. The proposed method is also capable of determining if no dynamicallyequivalent weakly reversible structure exists for a given reaction network witha previously fixed complex set.

Finding weakly reversible realizations of chemical reaction networks using optimization