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VertexContract[g,{v1,v2,…}]

contracts a collection of vertices v1, v2, … into a single vertex of the graph g.

VertexContract[g,{{v1,v2,…},…}]

contracts several collections of vertices.

VertexContract[{vw,…},…]

uses rules vw to specify the graph g.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
See Also
Related Guides
History
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VertexContract

VertexContract[g,{v1,v2,…}]

contracts a collection of vertices v1, v2, … into a single vertex of the graph g.

VertexContract[g,{{v1,v2,…},…}]

contracts several collections of vertices.

VertexContract[{vw,…},…]

uses rules vw to specify the graph g.

Details and Options

  • VertexContract is also known as vertex identification.
  • VertexContract[g,{v1,v2,…}] creates a new graph from g by removing all edges between vi and vj and merging them into the single vertex v1.
  • VertexContract works with undirected graphs, directed graphs, multigraphs, and mixed graphs.

Examples

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Basic Examples  (1)

Contract vertices of a graph:

Scope  (7)

VertexContract works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

Use patterns to specify a set of vertices:

VertexContract works with large graphs:

Applications  (2)

Find the connectivity between communities in a network:

Condensation graph:

List all possible vertex identifications between two RNA tree models to model RNA bonding:

Gather all isomorphic graphs into groups and show non-isomorphic trees:

Properties & Relations  (2)

Using VertexReplace to contract vertices:

EdgeContract can be computed using VertexContract:

Wolfram Research (2014), VertexContract, Wolfram Language function, https://reference.wolfram.com/language/ref/VertexContract.html (updated 2015).

Text

Wolfram Research (2014), VertexContract, Wolfram Language function, https://reference.wolfram.com/language/ref/VertexContract.html (updated 2015).

CMS

Wolfram Language. 2014. "VertexContract." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/VertexContract.html.

APA

Wolfram Language. (2014). VertexContract. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/VertexContract.html

BibTeX

@misc{reference.wolfram_2025_vertexcontract, author="Wolfram Research", title="{VertexContract}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/VertexContract.html}", note=[Accessed: 14-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_vertexcontract, organization={Wolfram Research}, title={VertexContract}, year={2015}, url={https://reference.wolfram.com/language/ref/VertexContract.html}, note=[Accessed: 14-August-2025]}