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#### A Graph Theoretical Approach for Testing Binomiality of Reversible Chemical Reaction Networks

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arXiv:2010.12615.pdf

(Preprint), 418KB

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##### Citation

Rahkooy, H., & Vargas Montero, C. (2020). A Graph Theoretical Approach for Testing Binomiality of Reversible Chemical Reaction Networks. Retrieved from https://arxiv.org/abs/2010.12615.

Cite as: https://hdl.handle.net/21.11116/0000-0007-B427-2

##### Abstract

We study binomiality of the steady state ideals of chemical reaction

networks. Considering rate constants as indeterminates, the concept of

unconditional binomiality has been introduced and an algorithm based on linear

algebra has been proposed in a recent work for reversible chemical reaction

networks, which has a polynomial time complexity upper bound on the number of

species and reactions. In this article, using a modified version of

species--reaction graphs, we present an algorithm based on graph theory which

performs by adding and deleting edges and changing the labels of the edges in

order to test unconditional binomiality. We have implemented our graph

theoretical algorithm as well as the linear algebra one in Maple and made

experiments on biochemical models. Our experiments show that the performance of

the graph theoretical approach is similar to or better than the linear algebra

approach, while it is drastically faster than Groebner basis and quantifier

elimination methods.

networks. Considering rate constants as indeterminates, the concept of

unconditional binomiality has been introduced and an algorithm based on linear

algebra has been proposed in a recent work for reversible chemical reaction

networks, which has a polynomial time complexity upper bound on the number of

species and reactions. In this article, using a modified version of

species--reaction graphs, we present an algorithm based on graph theory which

performs by adding and deleting edges and changing the labels of the edges in

order to test unconditional binomiality. We have implemented our graph

theoretical algorithm as well as the linear algebra one in Maple and made

experiments on biochemical models. Our experiments show that the performance of

the graph theoretical approach is similar to or better than the linear algebra

approach, while it is drastically faster than Groebner basis and quantifier

elimination methods.