The command NonEmptyPowerSet(S) returns the hypergraph with the set S as vertex set and  with all non-empty subsets of S as hyperedges.

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

$\mathrm{P4}≔\mathrm{NonEmptyPowerSet}\left(\left\{1\,2\,3\,4\right\}\right)$

$\mathrm{P4}≔\mathrm{<\; a\; hypergraph\; on\; 4\; vertices\; with\; 15\; hyperedges\; >}$

$\mathrm{Draw}\left(\mathrm{P4}\right)$

$M≔\mathrm{Min}\left(\mathrm{P4}\right)\&semi;$$\mathrm{Vertices}\left(M\right)\&semi;$$\mathrm{Hyperedges}\left(M\right)$

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

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

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

$M≔\mathrm{Max}\left(\mathrm{P4}\right)\&semi;$$\mathrm{Vertices}\left(M\right)\&semi;$$\mathrm{Hyperedges}\left(M\right)$

$M≔\mathrm{<\; a\; hypergraph\; on\; 4\; vertices\; with\; 1\; hyperedges\; >}$

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

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

$\mathrm{P8}≔\mathrm{NonEmptyPowerSet}\left(\left\{1\&comma;2\&comma;3\&comma;4\&comma;5\&comma;6\&comma;7\&comma;8\right\}\right)$

$\mathrm{P8}≔\mathrm{<\; a\; hypergraph\; on\; 8\; vertices\; with\; 255\; hyperedges\; >}$

$\mathrm{Draw}\left(\mathrm{P8}\right)$

$M≔\mathrm{Min}\left(\mathrm{P8}\right)\&semi;$$\mathrm{Vertices}\left(M\right)\&semi;$$\mathrm{Hyperedges}\left(M\right)$

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

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

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

$M≔\mathrm{Max}\left(\mathrm{P8}\right)\&semi;$$\mathrm{Vertices}\left(M\right)\&semi;$$\mathrm{Hyperedges}\left(M\right)$

$M≔\mathrm{<\; a\; hypergraph\; on\; 8\; vertices\; with\; 1\; hyperedges\; >}$

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

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

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[ExampleHypergraphs][NonEmptyPowerSet] command was introduced in Maple 2024.

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