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VertexList
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VertexList

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gives the list of vertices for the graph g.

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VertexList[g,patt]

gives a list of vertices that match the pattern patt.

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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

open allclose all

Basic Examples  (3)Summary of the most common use cases

The vertex list for an explicitly constructed graph:

In[1]:=1
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https://wolfram.com/xid/0bdp8tpkq-f8diwi
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bdp8tpkq-kk0qbl
Out[2]=2

The vertex list for a parametrically constructed graph:

In[1]:=1
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https://wolfram.com/xid/0bdp8tpkq-muw21
Out[1]=1

Find all vertices that match a pattern:

In[1]:=1
✖
https://wolfram.com/xid/0bdp8tpkq-tncjj
Out[1]=1

Scope  (5)Survey of the scope of standard use cases

VertexList works with undirected graphs:

In[2]:=2
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https://wolfram.com/xid/0bdp8tpkq-2n22nw
Out[2]=2

Directed graphs:

In[1]:=1
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https://wolfram.com/xid/0bdp8tpkq-lkwx7m
Out[1]=1

Use rules to specify the graph:

In[1]:=1
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https://wolfram.com/xid/0bdp8tpkq-bndh30
Out[1]=1

Use patterns to select a subset of vertices:

In[1]:=1
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https://wolfram.com/xid/0bdp8tpkq-53nmq
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bdp8tpkq-bp7bob
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0bdp8tpkq-ztobs
Out[3]=3

VertexList works with large graphs:

In[1]:=1
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https://wolfram.com/xid/0bdp8tpkq-pq9ae
In[2]:=2
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https://wolfram.com/xid/0bdp8tpkq-pt10p8
Out[2]=2

Applications  (2)Sample problems that can be solved with this function

Find all vertices with a given annotation:

In[1]:=1
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https://wolfram.com/xid/0bdp8tpkq-obof4g
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bdp8tpkq-31ufl
Out[2]=2

Highlight the vertex by the vertex degree:

In[1]:=1
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https://wolfram.com/xid/0bdp8tpkq-ebd33q
In[2]:=2
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https://wolfram.com/xid/0bdp8tpkq-rzl9c
In[3]:=3
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https://wolfram.com/xid/0bdp8tpkq-capbob
Out[3]=3

Properties & Relations  (7)Properties of the function, and connections to other functions

VertexCount can be found using VertexList:

In[1]:=1
✖
https://wolfram.com/xid/0bdp8tpkq-rtzao
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0bdp8tpkq-cnrlqt
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0bdp8tpkq-dw7ac3
Out[3]=3

VertexIndex gives the position of a vertex in VertexList:

In[1]:=1
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https://wolfram.com/xid/0bdp8tpkq-b6i6tc
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bdp8tpkq-d0o81c
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0bdp8tpkq-h7d8sv
Out[3]=3

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

In[1]:=1
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https://wolfram.com/xid/0bdp8tpkq-qsow
In[2]:=2
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https://wolfram.com/xid/0bdp8tpkq-g8zbu0
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0bdp8tpkq-qxa53
Out[3]=3

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

In[1]:=1
✖
https://wolfram.com/xid/0bdp8tpkq-hwzj2q
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0bdp8tpkq-ja4d8
Out[2]=2

The order can be modified with an explicit vertex list:

In[3]:=3
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https://wolfram.com/xid/0bdp8tpkq-deck35
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0bdp8tpkq-tx5ww
Out[4]=4

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

In[1]:=1
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https://wolfram.com/xid/0bdp8tpkq-kwmhmh
In[2]:=2
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https://wolfram.com/xid/0bdp8tpkq-cwu88m
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0bdp8tpkq-i573me

Rows of the incidence matrix correspond to VertexList:

In[1]:=1
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https://wolfram.com/xid/0bdp8tpkq-x999l1
In[2]:=2
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https://wolfram.com/xid/0bdp8tpkq-ip9ho
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0bdp8tpkq-dry0v4

Vertices can be specified in Graph:

In[1]:=1
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https://wolfram.com/xid/0bdp8tpkq-lj1md
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bdp8tpkq-bc25r2
Out[2]=2

AdjacencyGraph:

In[3]:=3
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https://wolfram.com/xid/0bdp8tpkq-l0kdv6
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0bdp8tpkq-iorx6k
Out[4]=4

IncidenceGraph:

In[5]:=5
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https://wolfram.com/xid/0bdp8tpkq-emj4u3
Out[5]=5
In[6]:=6
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https://wolfram.com/xid/0bdp8tpkq-cikafm
Out[6]=6
Wolfram Research (2010), VertexList, Wolfram Language function, https://reference.wolfram.com/language/ref/VertexList.html (updated 2015).
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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).

✖
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.

✖
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

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

BibTeX

@misc{reference.wolfram_2025_vertexlist, author="Wolfram Research", title="{VertexList}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/VertexList.html}", note=[Accessed: 10-July-2025 ]}

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@misc{reference.wolfram_2025_vertexlist, author="Wolfram Research", title="{VertexList}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/VertexList.html}", note=[Accessed: 10-July-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_vertexlist, organization={Wolfram Research}, title={VertexList}, year={2015}, url={https://reference.wolfram.com/language/ref/VertexList.html}, note=[Accessed: 10-July-2025 ]}

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@online{reference.wolfram_2025_vertexlist, organization={Wolfram Research}, title={VertexList}, year={2015}, url={https://reference.wolfram.com/language/ref/VertexList.html}, note=[Accessed: 10-July-2025 ]}