# FindMaximumCut

gives the maximum cut of the graph g.

# Details and Options

• FindMaximumCut is also known as the max-cut problem.
• Typically used in cluster analysis, VLSI design and statistical physics.
• A maximum cut of a graph g is a partition of the vertices of g into two disjoint subsets with the largest number of edges between them.
• FindMaximumCut returns a list of the form {cmin,{c1,c2}}, where cmin is the value of a maximum cut found, and {c1,c2} is a partition of the vertices for which it is found.
• For weighted graphs, FindMaximumCut gives a partition {c1,c2} with the largest sum of edge weights possible between the sets ci.
• The following options can be given:
•  EdgeWeight Automatic edge weight for each edge PerformanceGoal "Speed" aspects of performance to try to optimize

# Examples

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## Basic Examples(1)

Find the maximum cut:

Highlight the cut:

## Scope(5)

FindMaximumCut works with undirected graphs:

Directed graphs:

Weighted graphs:

Multigraphs:

Mixed 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(1)

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

The maximum cut:

Wolfram Research (2020), FindMaximumCut, Wolfram Language function, https://reference.wolfram.com/language/ref/FindMaximumCut.html.

#### Text

Wolfram Research (2020), FindMaximumCut, Wolfram Language function, https://reference.wolfram.com/language/ref/FindMaximumCut.html.

#### CMS

Wolfram Language. 2020. "FindMaximumCut." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FindMaximumCut.html.

#### APA

Wolfram Language. (2020). FindMaximumCut. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindMaximumCut.html

#### BibTeX

@misc{reference.wolfram_2024_findmaximumcut, author="Wolfram Research", title="{FindMaximumCut}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/FindMaximumCut.html}", note=[Accessed: 21-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_findmaximumcut, organization={Wolfram Research}, title={FindMaximumCut}, year={2020}, url={https://reference.wolfram.com/language/ref/FindMaximumCut.html}, note=[Accessed: 21-July-2024 ]}