This sort of thing intrigues me tremendously and I'm going over the text. At the same time, I always have a certain "what could you really get" feeling about systems that begin with machinery from objects with lots of structure (differentiable manifolds) and generalize and generalize until it is dealing a structure that seems utterly arbitrary. I mean, locally, "almost everywhere" (and similar caveats), the characteristics of a point of a differentiable manifold determine "nearly everything" about the points in its neighborhood. Oppositely, one node of graph no necessary relation to the next node.
So what exactly do we get from our complex machinery? Are the theorem ultimately more about "summation processes on graphs" than graphs?
