ABSTRACT
All of the discrete models we have seen so far – digraphs, graphs, preorders,
partial orders – have involved only binary relations. The next step up is to hy-
pergraphs (sometimes called set systems), which are discrete structures on
a set V where the edges are subsets of the power set of V . Hypergraphs orig-
inally received attention for their role as models. Designs are arrangements
of objects subject to particular regularity constraints. Point set topology
is essentially the study of hypergraphs closed under finite intersection and ar-
bitrary union. Finite geometry examines hypergraphs that satisfy a variety
of axioms related to Euclidean geometry. And we shall study one of the most
important classes of hypergraphs, namely simplicial complexes in the next
chapter.
