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# Blog - network theory (part 23)

In this post:

I'll show how any graph with positive numbers attached to its edges gives a Markov process, and write down a nice formula for the Hamiltonian of this Markov process:

$$H = \partial s^\dagger$$ Then I'll classify the equilibria of this process, at least when the graph is 'weakly reversible'. This is yet another step toward proving the zero deficiency theorem.

Comment Source:Well, I'm done with * [[Blog - network theory (part 23)]] now! The first theorem here must be incredibly well-known - it's a basic fact about Markov processes. When I write the book, I'll push this much earlier, so I can just _use_ it here. It's interesting in its own right, but getting it done sooner will make the proof of the deficiency zero theorem a lot easier to follow. I feel I'm just learning now how the whole series should have been written.