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TreeGraphQ[g]

yields True if the graph g is a tree and False otherwise.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Properties & Relations  
Possible Issues  
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TreeGraphQ

TreeGraphQ[g]

yields True if the graph g is a tree and False otherwise.

Details

  • A tree is a simple connected graph with no cycles.

Examples

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Basic Examples  (2)

Test whether a graph is a tree:

Wolfram Language code: Graph[{12, 13, 24, 25}]
Wolfram Language code: TreeGraphQ[%]
Wolfram Language code: CompleteKaryTree[2, 2]
Wolfram Language code: TreeGraphQ[%]
Wolfram Language code: AdjacencyGraph[{{0, 1, 1}, {0, 0, 0}, {0, 0, 0}}]
Wolfram Language code: TreeGraphQ[%]

A graph with cycles is not a tree:

Wolfram Language code: CycleGraph[5]
Wolfram Language code: TreeGraphQ[%]

Scope  (6)

TreeGraphQ works with undirected graphs:

Wolfram Language code: TreeGraphQ[[image]]

Directed graphs:

Wolfram Language code: TreeGraphQ[[image]]

Multigraphs:

Wolfram Language code: TreeGraphQ[[image]]

Mixed graphs:

Wolfram Language code: TreeGraphQ[[image]]

TreeGraphQ gives False for anything that is not a tree graph:

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

TreeGraphQ works with large graphs:

Wolfram Language code: g = GridGraph[{1, 1000000}];
Wolfram Language code: TreeGraphQ[g]//Timing
Wolfram Language code: {VertexCount[g], EdgeCount[g]}

Properties & Relations  (10)

A tree graph can be a simple graph:

Wolfram Language code: CompleteKaryTree[2, 3]
Wolfram Language code: {TreeGraphQ[%], SimpleGraphQ[%]}

A tree graph can be a weighted graph:

Wolfram Language code: CompleteKaryTree[2, 3, VertexWeight -> RandomInteger[5, 4]]
Wolfram Language code: {TreeGraphQ[%], WeightedGraphQ[%]}

A star is a special tree with as many leaves as possible:

Wolfram Language code: StarGraph[10]
Wolfram Language code: TreeGraphQ[%]

A path graph with no repeated vertices is a tree with two leaves:

Wolfram Language code: GridGraph[{1, 5}]
Wolfram Language code: {PathGraphQ[%], TreeGraphQ[%]}

A graph with self-loops is not a tree graph:

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

A graph with cycles is not a tree graph:

Wolfram Language code: CycleGraph[3]
Wolfram Language code: TreeGraphQ[%]

A disconnected graph is not a tree graph:

Wolfram Language code: Graph[{12, 23, 31, 45}]
Wolfram Language code: {ConnectedGraphQ[%], TreeGraphQ[%]}

A tree graph with vertices has edges:

Wolfram Language code: CompleteKaryTree[3, 3]
Wolfram Language code: VertexCount[%] - EdgeCount[%]

A tree graph is a bipartite graph:

Wolfram Language code: BipartiteGraphQ[CompleteKaryTree[3, 3]]

A tree graph is not Hamiltonian:

Wolfram Language code: HamiltonianGraphQ[CompleteKaryTree[3, 3]]

Possible Issues  (1)

TreeGraphQ gives False for non-explicit graphs:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_treegraphq, author="Wolfram Research", title="{TreeGraphQ}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/TreeGraphQ.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_treegraphq, organization={Wolfram Research}, title={TreeGraphQ}, year={2010}, url={https://reference.wolfram.com/language/ref/TreeGraphQ.html}, note=[Accessed: 13-June-2026]}