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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,….

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,….

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

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

VertexInComponentGraph[{vw,…},…]

uses rules vw to specify the graph g.

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

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,….

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,….

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

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

VertexInComponentGraph[{vw,…},…]

uses rules vw to specify the graph g.

Details and Options

Examples

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Basic Examples  (3)

Find the in-component graph of a vertex:

Wolfram Language code: g = [image];
Wolfram Language code: VertexInComponentGraph[g, {3}]

Highlight the in-component graph of a vertex:

Wolfram Language code: HighlightGraph[g, %]

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

Wolfram Language code: VertexInComponentGraph[[image], {3, 4}]

Highlight the in-component graph of a vertex:

Wolfram Language code: g = GridGraph[{5, 5}, VertexSize -> Medium, DirectedEdges -> True, EdgeStyle -> Arrowheads[Small]];
Wolfram Language code: Table[HighlightGraph[g, {Style[19, Blue], VertexInComponentGraph[g, {19}, i]}], {i, 3}]

Scope  (9)

VertexInComponentGraph works with undirected graphs:

Wolfram Language code: VertexInComponentGraph[[image], {1}]

Directed graphs:

Wolfram Language code: VertexInComponentGraph[[image], {2}]

Multigraphs:

Wolfram Language code: VertexInComponentGraph[[image], {6}]

Mixed graphs:

Wolfram Language code: VertexInComponentGraph[[image], {2}]

Tagged graphs:

Wolfram Language code: VertexInComponentGraph[[image], {1}]

Use rules to specify the graph:

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

Use patterns to select a subset of vertices:

Wolfram Language code: VertexInComponentGraph[[image], _ ? EvenQ]

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

Wolfram Language code: VertexInComponentGraph[[image], 6, 2]

VertexInComponentGraph works with large graphs:

Wolfram Language code: g = GridGraph[{10, 10, 10, 10}];
Wolfram Language code: VertexInComponentGraph[g, {1}] //VertexCount// Timing

Applications  (2)

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

Wolfram Language code: g = ExampleData[{"NetworkGraph", "EmailListMathGroup"}];
Wolfram Language code: s = Table[Length[VertexInComponent[g, v]], {v, VertexList[g]}];
Wolfram Language code: v = Pick[VertexList[g], s, Max[s]]

The most interesting subject of the month:

Wolfram Language code: PropertyValue[{g, First[v]}, "Subject"]

Show the network generated by this message:

Wolfram Language code: VertexInComponentGraph[g, v]

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:

Wolfram Language code: m = (⁠| | | | | | | | --- | --- | --- | --- | --- | --- | | 1 | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 0 | 1 | 0 | | 0 | 0 | 0.2 | 0.5 | 0.3 | 0 | | 0.7 | 0 | 0 | 0 | 0 | 0.3 | | 0 | 0.6 | 0 | 0 | 0.4 | 0 | | 0.8 | 0 | 0 | 0.2 | 0 | 0 |⁠);

Construct the state transition diagram of a transition matrix:

Wolfram Language code: g = AdjacencyGraph[Unitize[m], VertexLabels -> Placed["Name", Center], VertexSize -> .35, EdgeStyle -> Arrowheads[.04], VertexStyle -> LightDarkSwitched[White, GrayLevel[0.2]]]

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

Wolfram Language code: VertexInComponentGraph[g, 4]

Properties & Relations  (1)

Use VertexInComponent to find the in-component graph:

Wolfram Language code: g = [image];
Wolfram Language code: VertexInComponent[g, {5}]
Wolfram Language code: Subgraph[g, %]
Wolfram Language code: VertexInComponentGraph[g, {5}]
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.

CMS

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

BibTeX

@misc{reference.wolfram_2026_vertexincomponentgraph, author="Wolfram Research", title="{VertexInComponentGraph}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/VertexInComponentGraph.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_vertexincomponentgraph, organization={Wolfram Research}, title={VertexInComponentGraph}, year={2021}, url={https://reference.wolfram.com/language/ref/VertexInComponentGraph.html}, note=[Accessed: 13-June-2026]}