I'm not saying that all hypergraphs - or all graphs - literally are bipartite graphs, I'm saying that you can construct a bipartite graph that represents the sa

I'm not saying that all hypergraphs - or all graphs - literally are bipartite graphs, I'm saying that you can construct a bipartite graph that represents the same structure as the hypergraph. Given the hypergraph: A -> (B, C) you can convert it to a bipartite graph by introducing an extra vertex of the second type to represent the hyper-edge: A -> e e -> B e -> C You can do the same thing starting from a "regular" graph, although it's kind of silly for most purposes; for the basic cycle, you'd have: A -> e1 e1 -> B B -> e2 e2 -> C C -> e3 e3 -> A I'd say that's a much more valid representation of the graph than the spanning tree, which is lossy (since you can't tell from [A, B, C] whether or not there's an edge C->A).