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VertexDelete[g,v]

makes a graph by deleting the vertex ν and all edges connected to v from the graph g.

VertexDelete[g,{v1,v2,…}]

deletes a collection of vertices from g.

VertexDelete[g,patt]

deletes all vertices that match the pattern patt.

VertexDelete[{vw,…},…]

uses rules vw to specify the graph g.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
See Also
Related Guides
History
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VertexDelete

VertexDelete[g,v]

makes a graph by deleting the vertex ν and all edges connected to v from the graph g.

VertexDelete[g,{v1,v2,…}]

deletes a collection of vertices from g.

VertexDelete[g,patt]

deletes all vertices that match the pattern patt.

VertexDelete[{vw,…},…]

uses rules vw to specify the graph g.

Details and Options

  • VertexDelete is also known as vertex removal.
  • VertexDelete[g,v] will delete the vertex v only if it is present in g.
  • VertexDelete works with undirected graphs, directed graphs, multigraphs, and mixed graphs.

Examples

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Basic Examples  (1)

Delete a vertex from a complete graph:

Wolfram Language code: VertexDelete[[image], 1]

Scope  (8)

VertexDelete works with undirected graphs:

Wolfram Language code: VertexDelete[[image], 2]

Directed graphs:

Wolfram Language code: VertexDelete[[image], 2]

Multigraphs:

Wolfram Language code: VertexDelete[[image], 2]

Mixed graphs:

Wolfram Language code: VertexDelete[[image], 2]

Delete a set of vertices from the graph:

Wolfram Language code: VertexDelete[[image], {4, 5}]

Use rules to specify the graph:

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

Use a pattern to delete a subset of vertices:

Wolfram Language code: VertexDelete[[image], _ ? (# > 3&)]

VertexDelete works with large graphs:

Wolfram Language code: g = GridGraph[{10, 10, 10, 10}];
Wolfram Language code: VertexDelete[g, 100];//Timing
Wolfram Research (2010), VertexDelete, Wolfram Language function, https://reference.wolfram.com/language/ref/VertexDelete.html (updated 2015).

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_vertexdelete, author="Wolfram Research", title="{VertexDelete}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/VertexDelete.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_vertexdelete, organization={Wolfram Research}, title={VertexDelete}, year={2015}, url={https://reference.wolfram.com/language/ref/VertexDelete.html}, note=[Accessed: 12-June-2026]}