The dual hypergraph is a hypergraph whose nodes are the original hyper-edges,
with hyper-edges indicating the original incidence. Essentially, the
incidence matrix of the dual hypergraph is the transpose of the original
incidence matrix.
References
Tyshkevich, R.I. and Zverovich, Vadim E,
Line hypergraphs,Discrete Mathematics,
161, 265--283,1996.