Given a directed graph there is a conventional well-studied way to make a C* algebra out of it. There may be other interesting ways to do this--but there is at least this one clear accepted way to do it. Try googling "graph c*-algebras" That's already kind of interesting because graphs (and higher analogs such as foams) are used to describe geometry. All we can know about a geometry (based on a finite number of observations, which incidentally are of discrete-spectrum type) is naturally described by such objects. So they are the natural way to represent geometries. On the other hand quantum field theory is naturally represented in terms of C* algebras---the axiomatic generalization of von Neumann algebras of observables. So an obvious way to go if you want a general covariant QFT, in other words a GCQFT is to inject the underlying geometry ALSO into the C* algebra, as well as the fields. This suggests we should be looking at a mathematical object which is simultaneously a spin network, or spin foam, AND a pair (M,ω) where M is a C* algebra and ω is a state defined on M. Essentially M is all the measurements LIVING on the particular graph/complex and ω is what we think their expectation/correlation values are. It means that it might be rewarding to look at the conventional way people have worked out to build a C* algebra corresponding to any given directed graph. I'll assemble the links. Anyone who has already studied this area please contribute links to any sources you found helpful.