# LuccioSamiComponents

gives the LuccioSami components of the graph g.

LuccioSamiComponents[g,{v1,v2,}]

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

LuccioSamiComponents[{vw,},]

uses rules vw to specify the graph g.

# Details

• LuccioSamiComponents is also known as an LS set.
• A LuccioSami component is a set of vertices where each proper subset has more ties to its complement within the set than to the outside.
• LuccioSamiComponents returns a list of components {c1,c2,}, where each component ci is given as a list of vertices.
• is equivalent to .
• LuccioSamiComponents works with undirected graphs, directed graphs, multigraphs, and mixed graphs.

# Examples

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## Basic Examples(1)

Give the LuccioSami components for a graph:

## Scope(6)

LuccioSamiComponents 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(1)

Highlight all LuccioSami components in a graph:

## Properties & Relations(2)

All LuccioSami components are lambda components:

The converse is not always true:

LuccioSami components are partially ordered by inclusion:

The corresponding directed acyclic graph:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_lucciosamicomponents, author="Wolfram Research", title="{LuccioSamiComponents}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/LuccioSamiComponents.html}", note=[Accessed: 14-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_lucciosamicomponents, organization={Wolfram Research}, title={LuccioSamiComponents}, year={2015}, url={https://reference.wolfram.com/language/ref/LuccioSamiComponents.html}, note=[Accessed: 14-July-2024 ]}