WOLFRAM

Wolfram Language & System Documentation Center

UndirectedGraphQ[g]

yields True if the graph g is an undirected graph and False otherwise.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Properties & Relations  
Possible Issues  
See Also
Related Guides
History
Cite this Page

UndirectedGraphQ

UndirectedGraphQ[g]

yields True if the graph g is an undirected graph and False otherwise.

Details

  • A graph is undirected if every edge in the graph is undirected.

Examples

open all close all

Basic Examples  (2)

Test whether a graph is undirected:

Wolfram Language code: Graph[{12, 23, 31}]
Wolfram Language code: UndirectedGraphQ[%]

UndirectedGraphQ gives False for inputs that are not undirected graphs:

Wolfram Language code: Graph[{12, 23, 31, 34}]
Wolfram Language code: UndirectedGraphQ[%]

Scope  (6)

UndirectedGraphQ works with undirected graphs:

Wolfram Language code: UndirectedGraphQ[[image]]

Directed graphs:

Wolfram Language code: UndirectedGraphQ[[image]]

Multigraphs:

Wolfram Language code: UndirectedGraphQ[[image]]

Mixed graphs:

Wolfram Language code: UndirectedGraphQ[[image]]

UndirectedGraphQ gives False for anything that is not an undirected graph:

Wolfram Language code: UndirectedGraphQ[x]
Wolfram Language code: UndirectedGraphQ[Graph[garbage]]

UndirectedGraphQ works with large graphs:

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

Properties & Relations  (5)

The empty graphs are undirected graphs:

Wolfram Language code: {EmptyGraphQ[[image]], UndirectedGraphQ[[image]]}

An undirected graph can have self-loops:

Wolfram Language code: Graph[{12, 22}]
Wolfram Language code: {UndirectedGraphQ[%], LoopFreeGraphQ[%]}

A graph is either undirected or directed:

Wolfram Language code: {g1, g2} = {Graph[{12, 13}], Graph[{12, 21}]}
Wolfram Language code: UndirectedGraphQ /@ {g1, g2}
Wolfram Language code: DirectedGraphQ /@ {g1, g2}

A symmetric adjacency matrix is interpreted to be an undirected graph:

Wolfram Language code: m = (| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |);
Wolfram Language code: SymmetricMatrixQ[m]
Wolfram Language code: UndirectedGraphQ[AdjacencyGraph[m]]

Use DirectedEdges->True to interpret it as a directed graph:

Wolfram Language code: UndirectedGraphQ[AdjacencyGraph[m, DirectedEdges -> True]]

The incidence matrix of an undirected graph has no negative entries:

Wolfram Language code: g = Graph[{12, 23, 31}]
Wolfram Language code: UndirectedGraphQ[g]
Wolfram Language code: IncidenceMatrix[g]//MatrixForm

Possible Issues  (1)

UndirectedGraphQ gives False for non-explicit graphs:

Wolfram Language code: UndirectedGraphQ[CompleteGraph[n]]
Wolfram Research (2010), UndirectedGraphQ, Wolfram Language function, https://reference.wolfram.com/language/ref/UndirectedGraphQ.html.

Text

Wolfram Research (2010), UndirectedGraphQ, Wolfram Language function, https://reference.wolfram.com/language/ref/UndirectedGraphQ.html.

CMS

Wolfram Language. 2010. "UndirectedGraphQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/UndirectedGraphQ.html.

APA

Wolfram Language. (2010). UndirectedGraphQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/UndirectedGraphQ.html

BibTeX

@misc{reference.wolfram_2026_undirectedgraphq, author="Wolfram Research", title="{UndirectedGraphQ}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/UndirectedGraphQ.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_undirectedgraphq, organization={Wolfram Research}, title={UndirectedGraphQ}, year={2010}, url={https://reference.wolfram.com/language/ref/UndirectedGraphQ.html}, note=[Accessed: 13-June-2026]}