Hypergraph

Remarks

Some authors allow repeated hyperedges or the empty hyperedge; others require $E$ to be a set. A graph is the same thing as a $2$-uniform hypergraph without repeated edges. Example: the Fano plane, with the $7$ points as vertices and the $7$ lines as hyperedges, is a $3$-uniform hypergraph, since each line has $3$ points. Non-example: $V = \set{1, 2, 3}$ with $E = \set{\set{1, 2}, \set{1, 2, 3}}$ is a hypergraph that is not $k$-uniform for any $k$, because its hyperedges have sizes $2$ and $3$. Every hypergraph has an incidence matrix, with a row for each vertex and a column for each hyperedge.