Generalization of graph where edges relate more than two vertices

Question

In traditional graph theory, a graph consists of a vertex set $V$ and an edge set $E$, where the elements of $E$ are pairs of vertices from $V$. Is there a name for "graphs" where the "edges" are triples for instance? Does this fall under design theory (e.g. Steiner triple system?) or is it called something else?

Answer 1

The term you need is hypergraph. Just the main thing is

A hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two vertices.