We introduce a unifying and generalizing framework for complex and detailedbalanced steady states in chemical reaction network theory. To this end, wegeneralize the graph commonly used to represent a reaction network.Specifically, we introduce a graph, called a reaction graph, that has one edgefor each reaction but potentially multiple nodes for each complex. A specialclass of steady states, called node balanced steady states, is naturallyassociated with such a reaction graph. We show that complex and detailedbalanced steady states are special cases of node balanced steady states bychoosing appropriate reaction graphs. Further, we show that node balancedsteady states have properties analogous to complex balanced steady states, suchas uniqueness and asymptotical stability in each stoichiometric compatibilityclass. Moreover, we associate an integer, called the deficiency, to a reactiongraph that gives the number of independent relations in the reaction rateconstants that need to be satisfied for a positive node balanced steady stateto exist. The set of reaction graphs (modulo isomorphism) is equipped with a partialorder that has the complex balanced reaction graph as minimal element. Werelate this order to the deficiency and to the set of reaction rate constantsfor which a positive node balanced steady state exists.
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