# LambdaComponents

gives the lambda components of the graph g.

LambdaComponents[g,{v1,v2,}]

gives the lambda components that include at least one of the vertices {v1,v2,}.

LambdaComponents[{vw,},]

uses rules vw to specify the graph g.

# Details

• LambdaComponents is also known as a lambda set.
• A lambda component is a set of vertices that have more edge-independent paths connecting them to each other than to outside vertices.
• LambdaComponents returns a list of components {c1,c2,}, where each component ci is given as a list of vertices.
• is equivalent to LambdaComponents[g,VertexList[g]].
• LambdaComponents works with undirected graphs, directed graphs, multigraphs, and mixed graphs.

# Examples

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## Basic Examples(1)

Give the lambda components for a graph:

## Scope(6)

LambdaComponents works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

Give the components that include at least one of the vertices:

Use rules to specify the graph:

## Applications(2)

Highlight all lambda components in a graph:

A family network consisting of the closest relatives, including parents, siblings, and children. Find a smallest family group with more than one member, where relatives have more edge-independent paths connecting them to each other than to relatives outside the group:

The first nontrivial λ component occurs after the singletons:

## Properties & Relations(2)

All LuccioSami components are lambda components:

The converse is not always true:

Lambda components are partially ordered by inclusion:

The corresponding directed acyclic graph:

Wolfram Research (2012), LambdaComponents, Wolfram Language function, https://reference.wolfram.com/language/ref/LambdaComponents.html (updated 2015).

#### Text

Wolfram Research (2012), LambdaComponents, Wolfram Language function, https://reference.wolfram.com/language/ref/LambdaComponents.html (updated 2015).

#### CMS

Wolfram Language. 2012. "LambdaComponents." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/LambdaComponents.html.

#### APA

Wolfram Language. (2012). LambdaComponents. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LambdaComponents.html

#### BibTeX

@misc{reference.wolfram_2024_lambdacomponents, author="Wolfram Research", title="{LambdaComponents}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/LambdaComponents.html}", note=[Accessed: 17-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_lambdacomponents, organization={Wolfram Research}, title={LambdaComponents}, year={2015}, url={https://reference.wolfram.com/language/ref/LambdaComponents.html}, note=[Accessed: 17-July-2024 ]}