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EdgeContract[g,e]

contracts the edge e of the graph g.

EdgeContract[g,{e1,e2,…}]

contracts a collection of edges e1,e2,….

EdgeContract[{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

EdgeContract

EdgeContract[g,e]

contracts the edge e of the graph g.

EdgeContract[g,{e1,e2,…}]

contracts a collection of edges e1,e2,….

EdgeContract[{vw,…},…]

uses rules vw to specify the graph g.

Details and Options

  • EdgeContract is also known as edge collapse.
  • EdgeContract[g,e] creates a new graph from g by deleting the edge e and merging vertices of e.
  • EdgeContract works with undirected graphs, directed graphs, multigraphs, and mixed graphs.

Examples

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Basic Examples  (1)

Contract edges of a graph:

Wolfram Language code: EdgeContract[[image], 12]

Scope  (7)

EdgeContract works with undirected graphs:

Wolfram Language code: EdgeContract[[image], 12]

Directed graphs:

Wolfram Language code: EdgeContract[[image], 21]

Multigraphs:

Wolfram Language code: EdgeContract[[image], 12]

Mixed graphs:

Wolfram Language code: EdgeContract[[image], 21]

Use rules to specify the graph:

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

Use patterns to specify a set of edges:

Wolfram Language code: EdgeContract[[image], 3_]

EdgeContract works with large graphs:

Wolfram Language code: GridGraph[{10, 10, 10, 10}];
Wolfram Language code: VertexCount[EdgeContract[%, {12}]]//Timing

Properties & Relations  (1)

EdgeContract can be computed using VertexContract:

Wolfram Language code: g = WheelGraph[7];
Wolfram Language code: EdgeContract[g, {12, 34}]
Wolfram Language code: VertexContract[g, Flatten[List@@@{12, 34}]]
Wolfram Research (2014), EdgeContract, Wolfram Language function, https://reference.wolfram.com/language/ref/EdgeContract.html (updated 2015).

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_edgecontract, author="Wolfram Research", title="{EdgeContract}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/EdgeContract.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_edgecontract, organization={Wolfram Research}, title={EdgeContract}, year={2015}, url={https://reference.wolfram.com/language/ref/EdgeContract.html}, note=[Accessed: 13-June-2026]}