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VertexAdd[g,v]

makes a graph by adding the vertex v to the graph g.

VertexAdd[g,{v1,v2,…}]

adds a collection of vertices to g.

VertexAdd[{vw,…},…]

uses rules vw to specify the graph g.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Properties & Relations  
See Also
Related Guides
History
Cite this Page

VertexAdd

VertexAdd[g,v]

makes a graph by adding the vertex v to the graph g.

VertexAdd[g,{v1,v2,…}]

adds a collection of vertices to g.

VertexAdd[{vw,…},…]

uses rules vw to specify the graph g.

Details and Options

  • VertexAdd is also known as vertex insertion.
  • VertexAdd[g,v] will add the vertex v only if it does not already exist in g.
  • VertexAdd works with undirected graphs, directed graphs, multigraphs, and mixed graphs.

Examples

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Basic Examples  (1)

Add a vertex to a complete graph:

Wolfram Language code: VertexAdd[[image], 6]

Scope  (7)

VertexAdd works with undirected graphs:

Wolfram Language code: VertexAdd[[image], 7]

Directed graphs:

Wolfram Language code: VertexAdd[[image], 7]

Multigraphs:

Wolfram Language code: VertexAdd[[image], 7]

Mixed graphs:

Wolfram Language code: VertexAdd[[image], 7]

Add a set of vertices to the graph:

Wolfram Language code: VertexAdd[[image], {7, 8}]

Use rules to specify the graph:

Wolfram Language code: VertexAdd[{1 -> 3, 2 -> 1, 3 -> 6, 4 -> 6, 1 -> 5, 5 -> 4, 6 -> 1}, 7]

VertexAdd works with large graphs:

Wolfram Language code: g = GridGraph[{10, 10, 10, 10}];
Wolfram Language code: VertexAdd[g, 100001];//Timing

Properties & Relations  (2)

VertexAdd does not change the EdgeList:

Wolfram Language code: EdgeList[[image]] == EdgeList[VertexAdd[[image], 5]]

The number of vertices can be found using VertexCount:

Wolfram Language code: g = PathGraph[Range[20]]
Wolfram Language code: VertexAdd[g, Range[21, 30]]
Wolfram Language code: VertexCount[%] - VertexCount[g]
Wolfram Research (2010), VertexAdd, Wolfram Language function, https://reference.wolfram.com/language/ref/VertexAdd.html (updated 2015).

Text

Wolfram Research (2010), VertexAdd, Wolfram Language function, https://reference.wolfram.com/language/ref/VertexAdd.html (updated 2015).

CMS

Wolfram Language. 2010. "VertexAdd." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/VertexAdd.html.

APA

Wolfram Language. (2010). VertexAdd. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/VertexAdd.html

BibTeX

@misc{reference.wolfram_2026_vertexadd, author="Wolfram Research", title="{VertexAdd}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/VertexAdd.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_vertexadd, organization={Wolfram Research}, title={VertexAdd}, year={2015}, url={https://reference.wolfram.com/language/ref/VertexAdd.html}, note=[Accessed: 13-June-2026]}