Existing graph-theoretic analysis would still apply to hypergraphs after essentially redefining the graph using coloring algorithms no?
> Hypergraphs can be viewed as incidence structures. In particular, there is a bipartite "incidence graph" or "Levi graph" corresponding to every hypergraph
Where the relation is one-to-one, so there is a Levi graph for every hypergraph and the reverse is also true.