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.

中文翻译：

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一种测试可逆化学反应网络二项式的图论方法

我们研究化学反应网络稳态理想的二项性。将速率常数视为不确定的，引入了无条件二项式的概念，并在最近的可逆化学反应网络工作中提出了一种基于线性代数的算法，该算法在物种和反应的数量上具有多项式时间复杂度上限。在本文中，使用物种反应图的修改版本，我们提出了一种基于图论的算法，该算法通过添加和删除边以及更改边的标签来测试无条件二项性。我们已经在 Maple 中实现了我们的图论算法以及线性代数算法，并在生化模型上进行了实验。