The command IsLinear(H) checks whether the hypergraph H is linear or not.

with(Hypergraphs): with(GraphTheory): with(ExampleHypergraphs):

H := Hypergraph([1,2,3,4,5,6,7], [{1,2,3}, {2,3}, {4}, {3,5,6}]);

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

Hypergraphs:-Vertices(H); Hyperedges(H);

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

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

Draw(H);

Hypergraphs:-IsConnected(H);

$\mathrm{false}$

IsLinear(H);

$\mathrm{false}$

L := Hypergraphs:-LineGraph(H);

$L≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 4\; vertices,\; 3\; edges,\; and\; 4\; self-loops}$

DrawGraph(L);

M := VertexEdgeIncidenceGraph(H);

$M≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 11\; vertices\; and\; 9\; edges}$

DrawGraph(M);

H := Lovasz(3);

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

Hypergraphs:-Vertices(H); Hyperedges(H);

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

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

Draw(H);

Hypergraphs:-IsConnected(H);

$\mathrm{true}$

IsLinear(H);

$\mathrm{false}$

L := Hypergraphs:-LineGraph(H);

$L≔\mathrm{Graph\; 3:\; an\; undirected\; graph\; with\; 10\; vertices,\; 45\; edges,\; and\; 10\; self-loops}$

DrawGraph(L);

M := VertexEdgeIncidenceGraph(H);

$M≔\mathrm{Graph\; 4:\; an\; undirected\; graph\; with\; 16\; vertices\; and\; 30\; edges}$

DrawGraph(M);

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[IsLinear] command was introduced in Maple 2024.

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