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.

翻译：我们研究化学反应网络稳定状态理想的二元性。考虑到比率常数作为不确定因素,我们引入了无条件二元性的概念,并在最近一项可逆化学反应网络的工作中提出了基于线性代数的算法,该算法在物种和反应数量上具有多元时间复杂性。在本条中,我们使用一个经过修改的物种反应图表版本,提出了一个基于图表理论的算法,通过增减边缘和改变边缘标签来进行演算法,以测试无条件二元性。我们已经在马普勒实施了我们的图表理论算法和线性代数模型,并进行了生物化学模型实验。我们的实验表明,图形理论方法的性能与线性变数法相似或更好,但比Groebner基础和量化法快得多。