WOLFRAM

Wolfram Language & System Documentation Center

VertexQ[g,v]

yields True if v is a vertex in the graph g and False otherwise.

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

VertexQ

VertexQ[g,v]

yields True if v is a vertex in the graph g and False otherwise.

Examples

open all close all

Basic Examples  (2)

Test whether an item is a vertex of a graph:

Wolfram Language code: CompleteGraph[5, VertexShapeFunction -> "Name"]
Wolfram Language code: VertexQ[%, 4]

Test items of various kinds:

Wolfram Language code: PetersenGraph[7, 2, VertexShapeFunction -> "Name"]
Wolfram Language code: {VertexQ[%, 15], VertexQ[%, "foo"], VertexQ[%, 12]}

Scope  (5)

VertexQ works with undirected graphs:

Wolfram Language code: VertexQ[[image], 15]

Directed graphs:

Wolfram Language code: VertexQ[[image], 2]

Multigraphs:

Wolfram Language code: VertexQ[[image], 2]

Mixed graphs:

Wolfram Language code: VertexQ[[image], 2]

VertexQ works with large graphs:

Wolfram Language code: g = GridGraph[{10, 10, 10, 10}];
Wolfram Language code: Timing[VertexQ[g, 10^6]]
Wolfram Language code: VertexCount[g]

Compare performance with a test based on VertexList:

Wolfram Language code: Timing[MemberQ[VertexList[g], 10^4]]

Applications  (3)

Check input to a function:

Wolfram Language code: styleOfVertex[g_ ? GraphQ, v_] /; VertexQ[g, v] := AnnotationValue[{g, v}, VertexStyle]
Wolfram Language code: {styleOfVertex[[image], 2], styleOfVertex[[image], 5]}

Take the correct action depending on whether an item is a vertex or an edge:

Wolfram Language code: g = CompleteGraph[4, VertexSize -> Small]
Wolfram Language code: makeRed[item_ /; VertexQ[g, item]] := AnnotationValue[{g, item}, VertexStyle] = Red
Wolfram Language code: makeRed[item_ /; EdgeQ[g, item]] := AnnotationValue[{g, item}, EdgeStyle] = Red

Act on a vertex:

Wolfram Language code: makeRed[1]; g

Act on an edge:

Wolfram Language code: makeRed[23]; g

Use Graph and VertexQ for fast set membership tests:

Wolfram Language code: elements = RandomInteger[10000, {1000}]; g = Graph[elements, {}];
Wolfram Language code: Timing[Count[Table[VertexQ[g, i], {i, 10000}], True]]

Compare with MemberQ:

Wolfram Language code: Timing[Count[Table[MemberQ[elements, i], {i, 10000}], True]]

Properties & Relations  (3)

VertexQ[g,v] is equivalent to MemberQ[VertexList[g],v]:

Wolfram Language code: g = Graph[{12, 23}];
Wolfram Language code: {MemberQ[VertexList[g], 2], VertexQ[g, 2]}

The performance of VertexQ is typically higher:

Wolfram Language code: g = GridGraph[{10, 10, 10, 10}];
Wolfram Language code: {Timing[MemberQ[VertexList[g], 2]], Timing[VertexQ[g, 2]]}

Use VertexIndex to find the position of a vertex in VertexList[g]:

Wolfram Language code: g = Graph[{34, 12, 24, 23}]
Wolfram Language code: VertexIndex[g, 2]

VertexIndex is typically faster than Position:

Wolfram Language code: g = GridGraph[{10, 10, 10, 10}];
Wolfram Language code: {Timing[VertexIndex[g, 2]], Timing[Position[VertexList[g], 2]]}

Use EdgeQ to test whether an edge is part of a graph:

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

Possible Issues  (1)

Some vertices do not seem to be recognized:

Wolfram Language code: v = Block[{ϵ = 10 ^ -15}, Range[1.0, 10.0] + ϵ]
Wolfram Language code: g = Graph[v, Table[v[[i]]v[[i + 1]], {i, 1, 9}]]
Wolfram Language code: VertexQ[g, 1.0]

Membership is tested using SameQ rather than Equal:

Wolfram Language code: {v[[1]] === 1.0, v[[1]] == 1.0}

By using identical expressions it can still be tested:

Wolfram Language code: VertexQ[g, v[[1]]]
Wolfram Research (2010), VertexQ, Wolfram Language function, https://reference.wolfram.com/language/ref/VertexQ.html.

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_vertexq, author="Wolfram Research", title="{VertexQ}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/VertexQ.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_vertexq, organization={Wolfram Research}, title={VertexQ}, year={2010}, url={https://reference.wolfram.com/language/ref/VertexQ.html}, note=[Accessed: 13-June-2026]}