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VertexInComponentGraph
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VertexInComponentGraph

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VertexInComponentGraph[g,{v1,v2,…}]

gives the subgraph of the graph g generated by the vertices that have a directed path to at least one of v1,v2,….

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VertexInComponentGraph[g,{v1,v2,…},k]

gives the subgraph of g generated by vertices with a directed path of at most length k to at least one of v1,v2,….

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VertexInComponentGraph[g,{v1,v2,…},{k}]

gives the subgraph of g generated by vertices of length exactly k.

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VertexInComponentGraph[{vw,…},…]

uses rules vw to specify the graph g.

Details and Options

Examples

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

Find the in-component graph of a vertex:

In[1]:=1
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https://wolfram.com/xid/0cf3zahhn5yum4q-8risxi
In[2]:=2
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https://wolfram.com/xid/0cf3zahhn5yum4q-rdo0e7
Out[2]=2

Highlight the in-component graph of a vertex:

In[3]:=3
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https://wolfram.com/xid/0cf3zahhn5yum4q-pjhv9j
Out[3]=3

Find the in-component graph of a set of vertices in a graph:

In[1]:=1
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https://wolfram.com/xid/0cf3zahhn5yum4q-r9zsrk
Out[1]=1

Highlight the in-component graph of a vertex:

In[1]:=1
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https://wolfram.com/xid/0cf3zahhn5yum4q-pa9bjd
In[2]:=2
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https://wolfram.com/xid/0cf3zahhn5yum4q-rpzc4x
Out[2]=2

Scope  (9)Survey of the scope of standard use cases

VertexInComponentGraph works with undirected graphs:

In[1]:=1
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https://wolfram.com/xid/0cf3zahhn5yum4q-3jjvc1
Out[1]=1

Directed graphs:

In[1]:=1
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https://wolfram.com/xid/0cf3zahhn5yum4q-zg3ksa
Out[1]=1

Multigraphs:

In[1]:=1
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https://wolfram.com/xid/0cf3zahhn5yum4q-w3859o
Out[1]=1

Mixed graphs:

In[1]:=1
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https://wolfram.com/xid/0cf3zahhn5yum4q-vbiq94
Out[1]=1

Tagged graphs:

In[1]:=1
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https://wolfram.com/xid/0cf3zahhn5yum4q-g06cb5
Out[1]=1

Use rules to specify the graph:

In[1]:=1
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https://wolfram.com/xid/0cf3zahhn5yum4q-bndh30
Out[1]=1

Use patterns to select a subset of vertices:

In[1]:=1
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https://wolfram.com/xid/0cf3zahhn5yum4q-bp7bob
Out[1]=1

Find the in-component graph connected to a vertex by a path of at most length 2 in a graph:

In[1]:=1
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https://wolfram.com/xid/0cf3zahhn5yum4q-imtbi
Out[1]=1

VertexInComponentGraph works with large graphs:

In[1]:=1
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https://wolfram.com/xid/0cf3zahhn5yum4q-wd8zhr
In[2]:=2
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https://wolfram.com/xid/0cf3zahhn5yum4q-gopv0s
Out[2]=2

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

Find the message generating the largest total number of messages in the network of email sent to the MathGroup list in November 2011:

In[1]:=1
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https://wolfram.com/xid/0cf3zahhn5yum4q-hrqjma
In[2]:=2
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https://wolfram.com/xid/0cf3zahhn5yum4q-go8k52
In[3]:=3
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https://wolfram.com/xid/0cf3zahhn5yum4q-7r9swl
Out[3]=3

The most interesting subject of the month:

In[4]:=4
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https://wolfram.com/xid/0cf3zahhn5yum4q-gcs5ks
Out[4]=4

Show the network generated by this message:

In[6]:=6
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https://wolfram.com/xid/0cf3zahhn5yum4q-m3mesp
Out[6]=6

Build a graph by states that can reach to state 4 within a finite step in a finite-state Markov chain with the following transition probability matrix:

In[1]:=1
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https://wolfram.com/xid/0cf3zahhn5yum4q-j1xr7i

Construct the state transition diagram of a transition matrix:

In[2]:=2
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https://wolfram.com/xid/0cf3zahhn5yum4q-ut712s
Out[2]=2

Build the graph by states that can reach to state 4:

In[3]:=3
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https://wolfram.com/xid/0cf3zahhn5yum4q-2i6ont
Out[3]=3

Properties & Relations  (1)Properties of the function, and connections to other functions

Use VertexInComponent to find the in-component graph:

In[6]:=6
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https://wolfram.com/xid/0cf3zahhn5yum4q-6kj2bx
In[7]:=7
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https://wolfram.com/xid/0cf3zahhn5yum4q-nzzif9
Out[7]=7
In[8]:=8
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https://wolfram.com/xid/0cf3zahhn5yum4q-yfb2ix
Out[8]=8
In[9]:=9
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https://wolfram.com/xid/0cf3zahhn5yum4q-ofknv7
Out[9]=9
Wolfram Research (2021), VertexInComponentGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/VertexInComponentGraph.html.
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Wolfram Research (2021), VertexInComponentGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/VertexInComponentGraph.html.

Text

Wolfram Research (2021), VertexInComponentGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/VertexInComponentGraph.html.

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Wolfram Research (2021), VertexInComponentGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/VertexInComponentGraph.html.

CMS

Wolfram Language. 2021. "VertexInComponentGraph." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/VertexInComponentGraph.html.

✖
Wolfram Language. 2021. "VertexInComponentGraph." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/VertexInComponentGraph.html.

APA

Wolfram Language. (2021). VertexInComponentGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/VertexInComponentGraph.html

✖
Wolfram Language. (2021). VertexInComponentGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/VertexInComponentGraph.html

BibTeX

@misc{reference.wolfram_2025_vertexincomponentgraph, author="Wolfram Research", title="{VertexInComponentGraph}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/VertexInComponentGraph.html}", note=[Accessed: 08-July-2025 ]}

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@misc{reference.wolfram_2025_vertexincomponentgraph, author="Wolfram Research", title="{VertexInComponentGraph}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/VertexInComponentGraph.html}", note=[Accessed: 08-July-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_vertexincomponentgraph, organization={Wolfram Research}, title={VertexInComponentGraph}, year={2021}, url={https://reference.wolfram.com/language/ref/VertexInComponentGraph.html}, note=[Accessed: 08-July-2025 ]}

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@online{reference.wolfram_2025_vertexincomponentgraph, organization={Wolfram Research}, title={VertexInComponentGraph}, year={2021}, url={https://reference.wolfram.com/language/ref/VertexInComponentGraph.html}, note=[Accessed: 08-July-2025 ]}