GraphUtilities`
GraphUtilities`

# Bicomponents

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

Bicomponents[g]

gives the biconnected components of the undirected graph g.

# Details and Options

• Bicomponents functionality is now available in the built-in Wolfram Language function KVertexConnectedComponents.
• To use Bicomponents, you first need to load the Graph Utilities Package using Needs["GraphUtilities`"].
• A biconnected component is a maximal subgraph that has no cutpoint, where a cutpoint is a vertex v such that the subgraph becomes disconnected if v and all its edges are removed.
• Bicomponents treats the input g as an undirected graph.

# Examples

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## Basic Examples(2)

This shows that a simple line with two vertices is biconnected:

Bicomponents has been superseded by KVertexConnectedComponents:

## Scope(1)

This defines a small graph:

The graph has four bicomponents, one for each cycle and two for the line joining the cycles:

## Properties & Relations(2)

This shows that a simple line with two vertices is biconnected:

This defines a graph:

This shows its biconnected components and connected components:

The result from WeakComponents is always smaller than that of Bicomponents:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_bicomponents, author="Wolfram Research", title="{Bicomponents}", year="2007", howpublished="\url{https://reference.wolfram.com/language/GraphUtilities/ref/Bicomponents.html}", note=[Accessed: 21-June-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_bicomponents, organization={Wolfram Research}, title={Bicomponents}, year={2007}, url={https://reference.wolfram.com/language/GraphUtilities/ref/Bicomponents.html}, note=[Accessed: 21-June-2024 ]}