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  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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