GraphUtilities`
GraphUtilities`

# 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:
•  Weighted False whether edges with higher weights are preferred when forming the maximal independent edge set

# Examples

## Basic Examples(2)

This defines a small graph:

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

MaximalIndependentEdgeSet has been superseded by FindIndependentEdgeSet:

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.

#### CMS

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

#### BibTeX

@misc{reference.wolfram_2024_maximalindependentedgeset, author="Wolfram Research", title="{MaximalIndependentEdgeSet}", year="2007", howpublished="\url{https://reference.wolfram.com/language/GraphUtilities/ref/MaximalIndependentEdgeSet.html}", note=[Accessed: 25-June-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_maximalindependentedgeset, organization={Wolfram Research}, title={MaximalIndependentEdgeSet}, year={2007}, url={https://reference.wolfram.com/language/GraphUtilities/ref/MaximalIndependentEdgeSet.html}, note=[Accessed: 25-June-2024 ]}