The command VertexEdgeIncidenceGraph(H) returns the vertex edge incidence graph of H as a graph object of the GraphTheory module.

$\mathrm{with}\left(\mathrm{Hypergraphs}\right)\:$$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$$\mathrm{with}\left(\mathrm{ExampleHypergraphs}\right)\:$

$H≔\mathrm{Hypergraph}\left(\left[1\,2\,3\,4\,5\,6\,7\right]\,\left[\left\{1\,2\,3\right\}\,\left\{2\,3\right\}\,\left\{4\right\}\,\left\{3\,5\,6\right\}\right]\right)$

$H≔\mathrm{<\; a\; hypergraph\; on\; 7\; vertices\; with\; 4\; hyperedges\; >}$

$\mathrm{Hypergraphs}:-\mathrm{Vertices}\left(H\right)\&semi;$$\mathrm{Hyperedges}\left(H\right)$

$\left[1\&comma;2\&comma;3\&comma;4\&comma;5\&comma;6\&comma;7\right]$

$\left[\left\{4\right\}\&comma;\left\{2\&comma;3\right\}\&comma;\left\{1\&comma;2\&comma;3\right\}\&comma;\left\{3\&comma;5\&comma;6\right\}\right]$

$\mathrm{Draw}\left(H\right)$

$\mathrm{Hypergraphs}:-\mathrm{IsConnected}\left(H\right)$

$\mathrm{false}$

$\mathrm{IsLinear}\left(H\right)$

$\mathrm{false}$

$L≔\mathrm{Hypergraphs}:-\mathrm{LineGraph}\left(H\right)$

$L≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 4\; vertices,\; 3\; edge(s),\; and\; 4\; self-loop(s)}$

$\mathrm{DrawGraph}\left(L\right)$

$M≔\mathrm{VertexEdgeIncidenceGraph}\left(H\right)$

$M≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 11\; vertices\; and\; 9\; edge(s)}$

$\mathrm{DrawGraph}\left(M\right)$

$H≔\mathrm{Lovasz}\left(3\right)$

$H≔\mathrm{<\; a\; hypergraph\; on\; 6\; vertices\; with\; 10\; hyperedges\; >}$

$\mathrm{Hypergraphs}:-\mathrm{Vertices}\left(H\right)\&semi;$$\mathrm{Hyperedges}\left(H\right)$

$\left[1\&comma;2\&comma;3\&comma;4\&comma;5\&comma;6\right]$

$\left[\left\{1\&comma;2\&comma;4\right\}\&comma;\left\{1\&comma;3\&comma;4\right\}\&comma;\left\{2\&comma;3\&comma;4\right\}\&comma;\left\{1\&comma;2\&comma;5\right\}\&comma;\left\{1\&comma;3\&comma;5\right\}\&comma;\left\{2\&comma;3\&comma;5\right\}\&comma;\left\{1\&comma;2\&comma;6\right\}\&comma;\left\{1\&comma;3\&comma;6\right\}\&comma;\left\{2\&comma;3\&comma;6\right\}\&comma;\left\{4\&comma;5\&comma;6\right\}\right]$

$\mathrm{Draw}\left(H\right)$

$\mathrm{Hypergraphs}:-\mathrm{IsConnected}\left(H\right)$

$\mathrm{true}$

$\mathrm{IsLinear}\left(H\right)$

$\mathrm{false}$

$L≔\mathrm{Hypergraphs}:-\mathrm{LineGraph}\left(H\right)$

$L≔\mathrm{Graph\; 3:\; an\; undirected\; graph\; with\; 10\; vertices,\; 45\; edge(s),\; and\; 10\; self-loop(s)}$

$\mathrm{DrawGraph}\left(L\right)$

$M≔\mathrm{VertexEdgeIncidenceGraph}\left(H\right)$

$M≔\mathrm{Graph\; 4:\; an\; undirected\; graph\; with\; 16\; vertices\; and\; 30\; edge(s)}$

$\mathrm{DrawGraph}\left(M\right)$

Claude Berge. Hypergraphes. Combinatoires des ensembles finis. 1987,  Paris, Gauthier-Villars, translated to English.

Claude Berge. Hypergraphs. Combinatorics of Finite Sets.  1989, Amsterdam, North-Holland Mathematical Library, Elsevier, translated from French.

Charles Leiserson, Liyun Li, Marc Moreno Maza and Yuzhen Xie " Parallel computation of the minimal elements of a poset." Proceedings of the 4th International Workshop on Parallel Symbolic Computation (PASCO) 2010: 53-62, ACM.

The Hypergraphs[VertexEdgeIncidenceGraph] command was introduced in Maple 2024.

For more information on Maple 2024 changes, see Updates in Maple 2024.