# FindMinimumCut

gives the minimum cut of the graph g.

FindMinimumCut[{vw,}]

uses rules vw to specify the graph g.

# Details and Options

• A minimum k-cut of a graph g is a partition of vertices of g into k disjoint subsets with the smallest number of edges between them.
• FindMinimumCut returns a list of the form {cmin,{c1,c2,}}, where cmin is the value of a minimum cut found, and {c1,c2,} is a partition of the vertices for which it is found.
• For weighted graphs, FindMinimumCut gives a partition {c1,c2,} with the smallest sum of edge weights possible between the sets ci.
• The following option can be given:
•  EdgeWeight Automatic edge weight for each edge

# Examples

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## Basic Examples(1)

Find the minimum cut:

Highlight the cut:

## Scope(7)

FindMinimumCut works with undirected graphs:

Directed graphs:

Weighted graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

FindMinimumCut works with large graphs:

## Options(1)

### EdgeWeight(1)

By default, the edge weight of an edge is taken to be its EdgeWeight property if available, otherwise 1:

Use EdgeWeight->weights to set the edge weight:

## Properties & Relations(3)

Use FindGraphPartition to find a cut with approximately equal-sized parts:

The minimum cut:

EdgeConnectivity is the same as the value of a minimum cut:

Use FindEdgeCut to obtain edges between cut sets:

Highlight the edges and cut sets:

Wolfram Research (2012), FindMinimumCut, Wolfram Language function, https://reference.wolfram.com/language/ref/FindMinimumCut.html (updated 2015).

#### Text

Wolfram Research (2012), FindMinimumCut, Wolfram Language function, https://reference.wolfram.com/language/ref/FindMinimumCut.html (updated 2015).

#### CMS

Wolfram Language. 2012. "FindMinimumCut." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/FindMinimumCut.html.

#### APA

Wolfram Language. (2012). FindMinimumCut. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindMinimumCut.html

#### BibTeX

@misc{reference.wolfram_2024_findminimumcut, author="Wolfram Research", title="{FindMinimumCut}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/FindMinimumCut.html}", note=[Accessed: 12-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_findminimumcut, organization={Wolfram Research}, title={FindMinimumCut}, year={2015}, url={https://reference.wolfram.com/language/ref/FindMinimumCut.html}, note=[Accessed: 12-September-2024 ]}