AddVertices - Maple Help
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Hypergraphs

  

AddVertices

  

Augment the vertex set of an hypergraph

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

AddVertices(H,S)

Parameters

H

-

Hypergraph

S

-

list

Description

• 

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.

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).

• 

Partial hypergraph : If H :=(X, Y) is a hypergraph and Z is a subset of Y, then (X, Z) is called the partial hypergraph of H induced by Z.

• 

Subhypergraph :  If H :=(X, Y) is a hypergraph,  S is a subset of X and Z is the subset of Y consisting of the hyperedges of X contained in S, then (S, Z) is called the subhypergraph of H induced by S.

Examples

Create a hypergraph from its vertices and edges.

(1)

Print its vertices and edges.

(2)

Draw a graphical representation of this hypergraph.

Construct a new hypergraph from H by adding a new vertex, namely 8.

(3)

Print the vertices and edges of K.

(4)

Draw a graphical representation of K.

Check whether {1,2,8} is a hyperedge of H.

(5)

Construct a new hypergraph from H by adding {1,2,4} as an hyperedge.

(6)

Print the vertices and edges of L.

(7)

Draw a graphical representation of L.

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[AddVertices] command was introduced in Maple 2024.

• 

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

See Also

Hypergraphs[AddHyperedges]

Hypergraphs[AddVertices]

Hypergraphs[DualHypergraph]

Hypergraphs[Hyperedges]

Hypergraphs[Hypergraph]

Hypergraphs[IsEdge]

Hypergraphs[NumberOfHyperedges]

Hypergraphs[NumberOfVertices]

Hypergraphs[PartialHypergraph]

Hypergraphs[SubHypergraph]

Hypergraphs[VertexEdgeIncidenceGraph]

Hypergraphs[Vertices]

 


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