The command AddVertices(H,S) returns the hypergraph L whose vertex set consists of the members of S and the vertices of H, and whose hyperedges are those of H.

Therefore, if V denotes the vertex set of H, then H is the subhypergraph of L induced by V.

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

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

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

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

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

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

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

$K≔\mathrm{AddVertices}\left(H\&comma;\left[8\right]\right)$

$K≔\mathrm{<\; a\; hypergraph\; on\; 8\; vertices\; with\; 4\; hyperedges\; >}$

$\mathrm{Vertices}\left(K\right)\&semi;$$\mathrm{Hyperedges}\left(K\right)$

$\left[1\&comma;2\&comma;3\&comma;4\&comma;5\&comma;6\&comma;7\&comma;8\right]$

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

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

$\mathrm{IsEdge}\left(H\&comma;\left\{1\&comma;2\&comma;8\right\}\right)$

$\mathrm{false}$

$L≔\mathrm{AddHyperedges}\left(K\&comma;\left[\left\{1\&comma;2\&comma;8\right\}\right]\right)$

$L≔\mathrm{<\; a\; hypergraph\; on\; 8\; vertices\; with\; 5\; hyperedges\; >}$

$\mathrm{Vertices}\left(L\right)\&semi;$$\mathrm{Hyperedges}\left(L\right)$

$\left[1\&comma;2\&comma;3\&comma;4\&comma;5\&comma;6\&comma;7\&comma;8\right]$

$\left[\left\{4\right\}\&comma;\left\{2\&comma;3\right\}\&comma;\left\{1\&comma;2\&comma;3\right\}\&comma;\left\{3\&comma;5\&comma;6\right\}\&comma;\left\{1\&comma;2\&comma;8\right\}\right]$

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

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[AddVertices] command was introduced in Maple 2024.

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