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MaximalIndependentEdgeSet

As of Version 10, all the functionality of the GraphUtilities package is built into the Wolfram System. »

MaximalIndependentEdgeSet[g]

gives a maximal independent edge set of an undirected graph g.

Details and Options

  • MaximalIndependentEdgeSet functionality is now available in the built-in Wolfram Language function FindIndependentEdgeSet.
  • To use MaximalIndependentEdgeSet, you first need to load the Graph Utilities Package using Needs["GraphUtilities`"].
  • MaximalIndependentEdgeSet gives an approximate maximal set of pairwise nonadjacent edges of g.
  • A maximal independent edge set of a graph is also called a maximal matching.
  • The following option can be given:
  • WeightedFalsewhether edges with higher weights are preferred when forming the maximal independent edge set

Examples

Basic Examples  (2)Summary of the most common use cases

In[1]:=1
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https://wolfram.com/xid/0jtkjspbhofnpfoxpmgbnr3-f7icyo

This defines a small graph:

In[2]:=2
✖
https://wolfram.com/xid/0jtkjspbhofnpfoxpmgbnr3-snp
In[3]:=3
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https://wolfram.com/xid/0jtkjspbhofnpfoxpmgbnr3-pne
Out[3]=3

This shows that the maximal independent edge set contains three edges:

In[4]:=4
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https://wolfram.com/xid/0jtkjspbhofnpfoxpmgbnr3-eor
Out[4]=4

MaximalIndependentEdgeSet has been superseded by FindIndependentEdgeSet:

In[1]:=1
✖
https://wolfram.com/xid/0jtkjspbhofnpfoxpmgbnr3-qs9cop
In[2]:=2
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https://wolfram.com/xid/0jtkjspbhofnpfoxpmgbnr3-1paa34
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0jtkjspbhofnpfoxpmgbnr3-kn8gbn
Out[3]=3
Wolfram Research (2007), MaximalIndependentEdgeSet, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/MaximalIndependentEdgeSet.html.
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Wolfram Research (2007), MaximalIndependentEdgeSet, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/MaximalIndependentEdgeSet.html.

Text

Wolfram Research (2007), MaximalIndependentEdgeSet, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/MaximalIndependentEdgeSet.html.

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Wolfram Research (2007), MaximalIndependentEdgeSet, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/MaximalIndependentEdgeSet.html.

CMS

Wolfram Language. 2007. "MaximalIndependentEdgeSet." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/GraphUtilities/ref/MaximalIndependentEdgeSet.html.

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Wolfram Language. 2007. "MaximalIndependentEdgeSet." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/GraphUtilities/ref/MaximalIndependentEdgeSet.html.

APA

Wolfram Language. (2007). MaximalIndependentEdgeSet. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/GraphUtilities/ref/MaximalIndependentEdgeSet.html

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Wolfram Language. (2007). MaximalIndependentEdgeSet. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/GraphUtilities/ref/MaximalIndependentEdgeSet.html

BibTeX

@misc{reference.wolfram_2025_maximalindependentedgeset, author="Wolfram Research", title="{MaximalIndependentEdgeSet}", year="2007", howpublished="\url{https://reference.wolfram.com/language/GraphUtilities/ref/MaximalIndependentEdgeSet.html}", note=[Accessed: 29-April-2025 ]}

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@misc{reference.wolfram_2025_maximalindependentedgeset, author="Wolfram Research", title="{MaximalIndependentEdgeSet}", year="2007", howpublished="\url{https://reference.wolfram.com/language/GraphUtilities/ref/MaximalIndependentEdgeSet.html}", note=[Accessed: 29-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_maximalindependentedgeset, organization={Wolfram Research}, title={MaximalIndependentEdgeSet}, year={2007}, url={https://reference.wolfram.com/language/GraphUtilities/ref/MaximalIndependentEdgeSet.html}, note=[Accessed: 29-April-2025 ]}

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@online{reference.wolfram_2025_maximalindependentedgeset, organization={Wolfram Research}, title={MaximalIndependentEdgeSet}, year={2007}, url={https://reference.wolfram.com/language/GraphUtilities/ref/MaximalIndependentEdgeSet.html}, note=[Accessed: 29-April-2025 ]}