Some definitions (from what I can tell):
- A multigraph is a graph where a node can connect via multiple edges.
- A hypergraph is a graph where a single edge can connect more than two nodes. Alternatively, there are nodeless edges available in this domain (not sure if nodeless edges occur in the base of graph theory).
And so there are presumably fusions, etc. In the base theory of graphs, it seems as if implementing the sethood relation by whatever is formally possible "at hand" gives us images of foundationalistic, coherentistic, and infinitistic epistemic graphs, and then there are hybrid positions (e.g. infinite-step loops). But what, if any, are the forms of solutions to the epistemic regress, that can be defined from multigraph and hypergraph theory in turn?
For example, use a graph with a finite number of nodes (let's just use two for ease of representation) but say that there are 200 multigraphical edges connecting them. Contrast this with a pair of nodes with only 10 such edges. The epistemic flavor of the pair is foundationalistic, but would judging the first pair to be a better solution to a local regress problem be more coherentistically seasoned? Or, rather, is the relationship between multigraphical concepts and the forms of epistemic regresses much of an aside from questions like foundationalism-vs.-coherentism?
Nodeless edges, and then multiplicities of these edges, also seem to represent a much more precise, if not totally alternative, form of possible solutions to regress problems, at least assuming that all such graph-theoretic concepts can be used to characterize epistemic concepts. But again, I'm not (yet) seeing much of a direct link to the base epistemic types.
Another way to frame the question: Alessio Moretti says that his "geometry of logic" is not just a newfangled graph theory. However, I don't know that he does or even can rule out multigraphical/hypergraphical characterizations of his theory. In fact, a universal Moretti object in which all the Moretti crystal-fractals for each type of logic occur "as one" would seem to be profitably describable in such terms, with a crystal (on whichever level) with n nodes (for n logical operators on that level) for a given logic-type LT1 having the crystal for some other LT2, with < n nodes, embedded in it as a subcrystal, and the embedding being via some of the overcrystal's nodes being multigraphically connected (the different edges carrying the operational differences between the logics of the overcrystal and its subcrystals).
NOTE: I have used the foundations-of-mathematics tag for this post on account of the role that graph theory plays in foundational studies of mathematics, e.g. in the formation of set theory, and because if graph theory is relevant to the regress problem in the given manner, then graph theory is relevant to the form of the very question of mathematical foundations anyway.
EDIT: so far, I have found this paper about something they call "uncertainty theory," which seems to be an epistemological matter on some level. But so they tie in hypergraph theory with this matter of uncertainty.
2: one of the first linked essays does bring up hypergraphs in this connection, although I didn't recall that it does (it's been a while since I read the full texts). See also Conifold's comment below for a possible example from C. S. Peirce's work (and keep Peirce's work in graph theory in mind overall).