Complex and detailed balancing of chemical reaction networks revisited

TL;DR

This paper revisits the concepts of complex and detailed balancing in chemical reaction networks using algebraic graph theory, providing new insights and a constructive condition for complex balancing verification.

Contribution

It introduces a new necessary and sufficient condition for complex balancing based on Kirchhoff's Matrix Tree theorem, enhancing the theoretical framework.

Findings

New constructive verification method for complex balancing

Clarification of Wegscheider conditions

Revised understanding of complex and detailed balancing

Abstract

The characterization of the notions of complex and detailed balancing for mass action kinetics chemical reaction networks is revisited from the perspective of algebraic graph theory, in particular Kirchhoff's Matrix Tree theorem for directed weighted graphs. This yields an elucidation of previously obtained results, in particular with respect to the Wegscheider conditions, and a new necessary and sufficient condition for complex balancing, which can be verified constructively.