# WeaklyConnectedGraphQ

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

open allclose all

## Basic Examples(2)

Test whether a graph is weakly connected:

A graph with isolated vertices is not weakly connected:

## Scope(6)

Test undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

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

WeaklyConnectedGraphQ works with large graphs:

## Properties & Relations(3)

A tree graph is weakly connected:

A path graph is weakly connected:

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

A path graph with vertices has exactly edges:

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_2023_weaklyconnectedgraphq, author="Wolfram Research", title="{WeaklyConnectedGraphQ}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/WeaklyConnectedGraphQ.html}", note=[Accessed: 17-April-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2023_weaklyconnectedgraphq, organization={Wolfram Research}, title={WeaklyConnectedGraphQ}, year={2012}, url={https://reference.wolfram.com/language/ref/WeaklyConnectedGraphQ.html}, note=[Accessed: 17-April-2024 ]}