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VertexList[g]

gives the list of vertices for the graph g.

VertexList[g,patt]

gives a list of vertices that match the pattern patt.

VertexList[{vw,…},…]

uses rules vw to specify the graph g.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
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VertexList

VertexList[g]

gives the list of vertices for the graph g.

VertexList[g,patt]

gives a list of vertices that match the pattern patt.

VertexList[{vw,…},…]

uses rules vw to specify the graph g.

Details

  • VertexList is also known as nodes or actors.
  • VertexList returns the list of vertices in the order used by the graph g.

Examples

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Basic Examples  (3)

The vertex list for an explicitly constructed graph:

Wolfram Language code: Graph[{ab, bc, ca}]
Wolfram Language code: VertexList[%]

The vertex list for a parametrically constructed graph:

Wolfram Language code: VertexList[[image]]

Find all vertices that match a pattern:

Wolfram Language code: VertexList[[image], _ ? (# > 2&)]

Scope  (5)

VertexList works with undirected graphs:

Wolfram Language code: VertexList[[image]]

Directed graphs:

Wolfram Language code: VertexList[[image]]

Use rules to specify the graph:

Wolfram Language code: VertexList[{1 -> 3, 2 -> 1, 3 -> 6, 4 -> 6, 1 -> 5, 5 -> 4, 6 -> 1}]

Use patterns to select a subset of vertices:

Wolfram Language code: g = Graph[{12, 21, a1, a2, b1, b2, bb}]
Wolfram Language code: VertexList[g, _Integer]
Wolfram Language code: VertexList[g, Except[_Integer]]

VertexList works with large graphs:

Wolfram Language code: g = GridGraph[{10, 10, 10, 10}];
Wolfram Language code: Timing[VertexList[g]//Length]

Applications  (2)

Find all vertices with a given annotation:

Wolfram Language code: g = CompleteGraph[5, VertexStyle -> {1 -> Red, 2 -> Blue, 3 -> Red}, VertexSize -> Small]
Wolfram Language code: VertexList[g, _ ? (AnnotationValue[{g, #}, VertexStyle] == Red&)]

Highlight the vertex by the vertex degree:

Wolfram Language code: g = GridGraph[{10, 10}, VertexSize -> Large];
Wolfram Language code: vd = VertexDegree[g];
Wolfram Language code: HighlightGraph[g, Table[Style[VertexList[g][[i]], ColorData["TemperatureMap"][vd[[i]] / Max[vd]]], {i, VertexCount[g]}]]

Properties & Relations  (7)

VertexCount can be found using VertexList:

Wolfram Language code: g = CompleteGraph[5]
Wolfram Language code: VertexCount[g]
Wolfram Language code: Length[VertexList[g]]

VertexIndex gives the position of a vertex in VertexList:

Wolfram Language code: g = Graph[{"a""c", "a""b", "b""c"}]
Wolfram Language code: Position[VertexList[g], "c"]
Wolfram Language code: VertexIndex[g, "c"]

Use VertexQ to test if a vertex is a member of VertexList:

Wolfram Language code: g = GridGraph[{3, 3}];
Wolfram Language code: MemberQ[VertexList[g], 8]
Wolfram Language code: VertexQ[g, 8]

Vertices are taken in the order they appear in the list of edges:

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

The order can be modified with an explicit vertex list:

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

Rows and columns of the adjacency matrix follow the order given by VertexList:

Wolfram Language code: g = [image];
Wolfram Language code: VertexList[g]
Wolfram Language code: TableForm[Normal@(a = AdjacencyMatrix[g]), TableHeadings -> {c = Style[#, Red]& /@ %, c}]

Rows of the incidence matrix correspond to VertexList:

Wolfram Language code: g = [image];
Wolfram Language code: VertexList[g]
Wolfram Language code: TableForm[Normal@(m = IncidenceMatrix[g]), TableHeadings -> {Style[#, Red]& /@ VertexList[g], EdgeList[g]}]

Vertices can be specified in Graph:

Wolfram Language code: Graph[{a, b, c}, {ab, bc, ca}]
Wolfram Language code: VertexList[%]

AdjacencyGraph:

Wolfram Language code: AdjacencyGraph[{a, b, c}, {{0, 1, 1}, {1, 0, 1}, {1, 1, 0}}]
Wolfram Language code: VertexList[%]

IncidenceGraph:

Wolfram Language code: IncidenceGraph[{a, b, c}, {{1, 1, 0}, {1, 0, 1}, {0, 1, 1}}]
Wolfram Language code: VertexList[%]
Wolfram Research (2010), VertexList, Wolfram Language function, https://reference.wolfram.com/language/ref/VertexList.html (updated 2015).

Text

Wolfram Research (2010), VertexList, Wolfram Language function, https://reference.wolfram.com/language/ref/VertexList.html (updated 2015).

CMS

Wolfram Language. 2010. "VertexList." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/VertexList.html.

APA

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

BibTeX

@misc{reference.wolfram_2026_vertexlist, author="Wolfram Research", title="{VertexList}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/VertexList.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_vertexlist, organization={Wolfram Research}, title={VertexList}, year={2015}, url={https://reference.wolfram.com/language/ref/VertexList.html}, note=[Accessed: 13-June-2026]}