More general edges in hypergraphs

Questions
1

I know things are already too complicated, but perhaps in a way they are too simple. Edges in hypergraphs are directed, which means they are 2-valued. Why not allow more general edges, like n-valued, continuous, vector/tensor valued, etc? I doubt particles are possible without topological singularities, and so far (though I haven’t investigated this much) it doesn’t seem to be possible–I am not impressed by “forbidden minors”.

2

Also, once a hypergraph has been iterated many times and spacetime emerges, is there any advantage to not using regular old lattice gauge theory? And if there is no advantage, it strengthens my claim above, that two-valued edges are too simple to account for gauge bosons.