  There is increasing focus on analyzing data represented as hypergraphs, which
are better able to express complex relationships amongst entities than are
graphs. Much of the critical information about hypergraph structure is
available only in the intersection relationships of the hyperedges, and so
forming the "intersection complex" of a hypergraph is quite valuable. This
identifies a valuable isomorphism between the intersection complex and the
"concept lattice" formed from taking the hypergraph's incidence matrix as a
"formal context": hypergraphs also generalize graphs in that their incidence
matrices are arbitrary Boolean matrices. This isomorphism allows connecting
discrete algorithms for lattices and hypergraphs, in particular s-walks or
s-paths on hypergraphs can be mapped to order theoretical operations on the
concept lattice. We give new algorithms for formal concept lattices and
hypergraph s-walks on concept lattices. We apply this to a large real-world
dataset and find deep lattices implying high interconnectivity and complex
geometry of hyperedges.
