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GraphQ[g]

yields True if g is a valid Graph object and False otherwise.

Examples  
Basic Examples  
Scope  
Properties & Relations  
Possible Issues  
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GraphQ

GraphQ[g]

yields True if g is a valid Graph object and False otherwise.

Examples

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Basic Examples  (2)

Test whether an object is a valid Graph object:

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

A Graphics object that contains a picture of a graph is not a valid Graph object:

Wolfram Language code: GraphPlot[{1 -> 2, 2 -> 3, 3 -> 1}]
Wolfram Language code: GraphQ[%]

Scope  (6)

GraphQ works with undirected graphs:

Wolfram Language code: GraphQ[[image]]

Directed graphs:

Wolfram Language code: GraphQ[[image]]

Multigraphs:

Wolfram Language code: GraphQ[[image]]

Mixed graphs:

Wolfram Language code: GraphQ[[image]]

GraphQ gives False for anything that is not a graph:

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

GraphQ works with large graphs:

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

Properties & Relations  (5)

Test whether a graph is directed or undirected:

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

Test whether a graph is simple:

Wolfram Language code: {Graph[{12}], Graph[{12, 22}]}
Wolfram Language code: SimpleGraphQ /@ %

A graph can have self-loops:

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

Test whether a graph is bipartite:

Wolfram Language code: {Graph[{12, 23, 31}], Graph[{12, 23}]}
Wolfram Language code: BipartiteGraphQ /@ %

Test whether a graph is weighted:

Wolfram Language code: {AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 0 | | 0 | 0 | 1 | | 1 | 0 | 0 |)], WeightedAdjacencyGraph[(| | | | | - | - | - | | ∞ | 1 | ∞ | | ∞ | ∞ | 3 | | 2 | ∞ | ∞ |)]}
Wolfram Language code: WeightedGraphQ /@ %

Possible Issues  (1)

GraphQ gives False for non-explicit graphs:

Wolfram Language code: GraphQ[CompleteGraph[n]]

For an explicit integer it is a graph object:

Wolfram Language code: GraphQ[CompleteGraph[5]]
Wolfram Research (2010), GraphQ, Wolfram Language function, https://reference.wolfram.com/language/ref/GraphQ.html.

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_graphq, author="Wolfram Research", title="{GraphQ}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/GraphQ.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_graphq, organization={Wolfram Research}, title={GraphQ}, year={2010}, url={https://reference.wolfram.com/language/ref/GraphQ.html}, note=[Accessed: 13-June-2026]}