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WeaklyConnectedGraphQ[g]

yields True if the graph g is weakly connected, and False otherwise.

Details
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Examples  
Basic Examples  
Scope  
Properties & Relations  
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WeaklyConnectedGraphQ

WeaklyConnectedGraphQ[g]

yields True if the graph g is weakly connected, and False otherwise.

Details

  • WeaklyConnectedGraphQ works for any graph object.
  • A graph is weakly connected if there is a sequence of edges joining every pair of vertices.
  • A graph is weakly connected if there is a sequence of edges joining every pair of vertices when the graph is considered undirected.

Examples

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Basic Examples  (2)

Test whether a graph is weakly connected:

Wolfram Language code: WeaklyConnectedGraphQ[[image]]

A graph with isolated vertices is not weakly connected:

Wolfram Language code: WeaklyConnectedGraphQ[[image]]

Scope  (6)

Test undirected graphs:

Wolfram Language code: WeaklyConnectedGraphQ[[image]]

Directed graphs:

Wolfram Language code: WeaklyConnectedGraphQ[[image]]

Multigraphs:

Wolfram Language code: WeaklyConnectedGraphQ[[image]]

Mixed graphs:

Wolfram Language code: WeaklyConnectedGraphQ[[image]]

WeaklyConnectedGraphQ gives False for anything that is not a weakly connected graph:

Wolfram Language code: WeaklyConnectedGraphQ[a]

WeaklyConnectedGraphQ works with large graphs:

Wolfram Language code: GridGraph[{10, 10, 10, 10}];
Wolfram Language code: WeaklyConnectedGraphQ[%]//Timing

Properties & Relations  (3)

A tree graph is weakly connected:

Wolfram Language code: TreeGraph[{12, 13, 14}]
Wolfram Language code: ConnectedGraphQ[%]

A path graph is weakly connected:

Wolfram Language code: PathGraph[Range[10]]
Wolfram Language code: WeaklyConnectedGraphQ[%]

The minimum number of edges in a weakly connected graph with vertices is :

Wolfram Language code: g = PetersenGraph[5, 2]
Wolfram Language code: WeaklyConnectedGraphQ[g]
Wolfram Language code: EdgeCount[g] ≥ VertexCount[g] - 1

A path graph with vertices has exactly edges:

Wolfram Language code: h = PathGraph[Range[10]]
Wolfram Language code: WeaklyConnectedGraphQ[h]
Wolfram Language code: EdgeCount[h]
Wolfram Research (2012), WeaklyConnectedGraphQ, Wolfram Language function, https://reference.wolfram.com/language/ref/WeaklyConnectedGraphQ.html.

Text

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

CMS

Wolfram Language. 2012. "WeaklyConnectedGraphQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/WeaklyConnectedGraphQ.html.

APA

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

BibTeX

@misc{reference.wolfram_2026_weaklyconnectedgraphq, author="Wolfram Research", title="{WeaklyConnectedGraphQ}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/WeaklyConnectedGraphQ.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_weaklyconnectedgraphq, organization={Wolfram Research}, title={WeaklyConnectedGraphQ}, year={2012}, url={https://reference.wolfram.com/language/ref/WeaklyConnectedGraphQ.html}, note=[Accessed: 13-June-2026]}