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WeakComponents

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

WeakComponents[g]

gives a list of all weakly connected components in the undirected graph g.

Details and Options

  • WeakComponents functionality is now available in the built-in Wolfram Language function WeaklyConnectedComponents.
  • To use WeakComponents, you first need to load the Graph Utilities Package using Needs["GraphUtilities`"].
  • A weakly connected component of a directed graph is a set of vertices such that for each pair of vertices, there is a path between them. The graph g is considered as undirected.

Examples

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

In[1]:=1
✖
https://wolfram.com/xid/0cgn0zidfztf-byy0c

This shows that the following graph has two weakly connected components:

In[2]:=2
✖
https://wolfram.com/xid/0cgn0zidfztf-o309o
In[3]:=3
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https://wolfram.com/xid/0cgn0zidfztf-joq4a6
Out[3]=3

WeakComponents has been superseded by WeaklyConnectedComponents:

In[1]:=1
✖
https://wolfram.com/xid/0cgn0zidfztf-qs9cop
In[2]:=2
✖
https://wolfram.com/xid/0cgn0zidfztf-s1us5t
Out[2]=2
Wolfram Research (2007), WeakComponents, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/WeakComponents.html.
✖
Wolfram Research (2007), WeakComponents, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/WeakComponents.html.

Text

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

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

CMS

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

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

APA

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

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

BibTeX

@misc{reference.wolfram_2025_weakcomponents, author="Wolfram Research", title="{WeakComponents}", year="2007", howpublished="\url{https://reference.wolfram.com/language/GraphUtilities/ref/WeakComponents.html}", note=[Accessed: 23-April-2025 ]}

✖
@misc{reference.wolfram_2025_weakcomponents, author="Wolfram Research", title="{WeakComponents}", year="2007", howpublished="\url{https://reference.wolfram.com/language/GraphUtilities/ref/WeakComponents.html}", note=[Accessed: 23-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_weakcomponents, organization={Wolfram Research}, title={WeakComponents}, year={2007}, url={https://reference.wolfram.com/language/GraphUtilities/ref/WeakComponents.html}, note=[Accessed: 23-April-2025 ]}

✖
@online{reference.wolfram_2025_weakcomponents, organization={Wolfram Research}, title={WeakComponents}, year={2007}, url={https://reference.wolfram.com/language/GraphUtilities/ref/WeakComponents.html}, note=[Accessed: 23-April-2025 ]}