# 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_2024_vertexcontract, author="Wolfram Research", title="{VertexContract}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/VertexContract.html}", note=[Accessed: 12-August-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_vertexcontract, organization={Wolfram Research}, title={VertexContract}, year={2015}, url={https://reference.wolfram.com/language/ref/VertexContract.html}, note=[Accessed: 12-August-2024 ]}