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FindMaximumCut

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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)Summary of the most common use cases

Find the maximum cut:

In[1]:=1
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https://wolfram.com/xid/0n4kzmwrw28-wq63ol
In[2]:=2
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https://wolfram.com/xid/0n4kzmwrw28-7l4t6
Out[2]=2

Highlight the cut:

In[3]:=3
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https://wolfram.com/xid/0n4kzmwrw28-6bqxxq
Out[3]=3

Scope  (5)Survey of the scope of standard use cases

FindMaximumCut works with undirected graphs:

In[1]:=1
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https://wolfram.com/xid/0n4kzmwrw28-cf8y58
Out[1]=1

Directed graphs:

In[1]:=1
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https://wolfram.com/xid/0n4kzmwrw28-w5x6ap
Out[1]=1

Weighted graphs:

In[1]:=1
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https://wolfram.com/xid/0n4kzmwrw28-ykb9h2
Out[1]=1

Multigraphs:

In[1]:=1
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https://wolfram.com/xid/0n4kzmwrw28-68ynlo
Out[1]=1

Mixed graphs:

In[1]:=1
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https://wolfram.com/xid/0n4kzmwrw28-s1cts9
Out[1]=1

Options  (1)Common values & functionality for each option

EdgeWeight  (1)

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

In[1]:=1
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https://wolfram.com/xid/0n4kzmwrw28-xjk9gx
Out[1]=1

Use EdgeWeight->weights to set the edge weight:

In[2]:=2
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https://wolfram.com/xid/0n4kzmwrw28-ztdl4i
Out[2]=2

Properties & Relations  (1)Properties of the function, and connections to other functions

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

In[1]:=1
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https://wolfram.com/xid/0n4kzmwrw28-obiug0
In[2]:=2
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https://wolfram.com/xid/0n4kzmwrw28-vv2j2r
Out[2]=2

The maximum cut:

In[3]:=3
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https://wolfram.com/xid/0n4kzmwrw28-k2y17h
Out[3]=3
Wolfram Research (2020), FindMaximumCut, Wolfram Language function, https://reference.wolfram.com/language/ref/FindMaximumCut.html.
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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.

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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.

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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

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

BibTeX

@misc{reference.wolfram_2025_findmaximumcut, author="Wolfram Research", title="{FindMaximumCut}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/FindMaximumCut.html}", note=[Accessed: 06-June-2025 ]}

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@misc{reference.wolfram_2025_findmaximumcut, author="Wolfram Research", title="{FindMaximumCut}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/FindMaximumCut.html}", note=[Accessed: 06-June-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_findmaximumcut, organization={Wolfram Research}, title={FindMaximumCut}, year={2020}, url={https://reference.wolfram.com/language/ref/FindMaximumCut.html}, note=[Accessed: 06-June-2025 ]}

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@online{reference.wolfram_2025_findmaximumcut, organization={Wolfram Research}, title={FindMaximumCut}, year={2020}, url={https://reference.wolfram.com/language/ref/FindMaximumCut.html}, note=[Accessed: 06-June-2025 ]}