Vertices - Maple Help

Hypergraphs

 Vertices
 Return the vertices of an hypergraph

 Calling Sequence Vertices(H)

Parameters

 H -

Description

 • The command Vertices(H) returns a list of the vertices of H.

Terminology

 • Hypergraph : mathematically, a hypergraph is a pair (X, Y) where X  is a finite set and Y is a set of non-empty subsets of X.
 • Vertices : the members of X are called the vertices of the hypergraph (X, Y).
 • Hyperedges : the members of Y are called the hyperedges (or simply edges) of  the hypergraph (X, Y).

Examples

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

Create a hypergraph from its vertices and edges.

 > $H≔\mathrm{Hypergraph}\left(\left[1,2,3,4,5,6,7\right],\left[\left\{1,2,3\right\},\left\{2,3\right\},\left\{4\right\},\left\{3,5,6\right\}\right]\right)$
 ${H}{≔}{\mathrm{< a hypergraph on 7 vertices with 4 hyperedges >}}$ (1)

Print its vertices and edges.

 > $\mathrm{Vertices}\left(H\right);$$\mathrm{Hyperedges}\left(H\right)$
 $\left[{1}{,}{2}{,}{3}{,}{4}{,}{5}{,}{6}{,}{7}\right]$
 $\left[\left\{{4}\right\}{,}\left\{{2}{,}{3}\right\}{,}\left\{{1}{,}{2}{,}{3}\right\}{,}\left\{{3}{,}{5}{,}{6}\right\}\right]$ (2)

Draw a graphical representation of this hypergraph.

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

Create another hypergraph from its edges.

 > $H≔\mathrm{Hypergraph}\left(\left[\left\{1,2,3\right\},\left\{2,3\right\},\left\{4\right\},\left\{3,5,6\right\}\right]\right)$
 ${H}{≔}{\mathrm{< a hypergraph on 6 vertices with 4 hyperedges >}}$ (3)

Print its vertices and edges.

 > $\mathrm{Vertices}\left(H\right);$$\mathrm{Hyperedges}\left(H\right)$
 $\left[{1}{,}{2}{,}{3}{,}{4}{,}{5}{,}{6}\right]$
 $\left[\left\{{4}\right\}{,}\left\{{2}{,}{3}\right\}{,}\left\{{1}{,}{2}{,}{3}\right\}{,}\left\{{3}{,}{5}{,}{6}\right\}\right]$ (4)

Draw a graphical representation of this hypergraph.

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

Create a third hypergraph from its vertices and bit vector encodings of its edges.

 > $H≔\mathrm{Hypergraph}\left(\left[1,2,3,4,5,6,7\right],\left[8,6,7,52\right]\right)$
 ${H}{≔}{\mathrm{< a hypergraph on 7 vertices with 4 hyperedges >}}$ (5)

Print its vertices and edges.

 > $\mathrm{Vertices}\left(H\right);$$\mathrm{Hyperedges}\left(H\right)$
 $\left[{1}{,}{2}{,}{3}{,}{4}{,}{5}{,}{6}{,}{7}\right]$
 $\left[\left\{{4}\right\}{,}\left\{{2}{,}{3}\right\}{,}\left\{{1}{,}{2}{,}{3}\right\}{,}\left\{{3}{,}{5}{,}{6}\right\}\right]$ (6)

Draw a graphical representation of this hypergraph.

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

References

 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.

Compatibility

 • The Hypergraphs[Vertices] command was introduced in Maple 2024.