FindMaximumCut

FindMaximumCut[g]

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 Automaticedge 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-December-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-December-2024 ]}