Real world applications of hypergraphs

There is a nice for image clustering using a hypergraph: http://vision.ucsd.edu/bpc/

The slides are here: http://vision.ucsd.edu/~sagarwal/bpc_cvpr05_slides.pdf

Although the algorithm did not become mainstream, it is an elegant illustration of the idea of links in hypergaphs and their meaning. I think that hypergraphs might be very useful in data mining.

Hypergraphs are representable as bipartite graphs, and bipartite graphs can be used to construct a hypergraph. This is really just saying that you can represent interactions between some form of actors either as vertices or as (hyper-)edges.

Once we recognize this equivalence, we can then conclude that hypergraphs are usable when you might otherwise use a bipartite graph, and that the analogs of graph algorithms are more directly to algorithms on bipartite graphs.

Mathematical models of product assembly from parts are based on hypergraphs. This is used in Computer-aided Manufacturing (CAM) systems to determine possible and optimal (in some sense) orders of assembly.