Foundations of Chemical Reaction Network Theory pp 309-320 | Cite as

# Complex Balancing

## Abstract

We come now to the idea of complex balancing, which serves as a precursor to the Deficiency Zero Theorem. It is an idea that was hardly obvious at the time that Horn and Jackson [109] proposed it and examined its deep consequences. At the very least, it required that they take seriously a reaction network’s standard diagram as a directed graph. This might seem natural now, especially in the context of this book. But hardly obvious in 1972 was the notion that the *vertices* (complexes) of that graph are important entities with a mathematical life of their own, having flows into and out of them—flows that, at an equilibrium, might or might not be in balance. It is a wonder that Horn and Jackson could first imagine and then prove that the presence of such balance has profound ramifications.

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