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VertexOutComponentGraph[g,{v1,v2,…}]

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

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

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

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

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

VertexOutComponentGraph[{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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VertexOutComponentGraph

VertexOutComponentGraph[g,{v1,v2,…}]

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

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

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

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

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

VertexOutComponentGraph[{vw,…},…]

uses rules vw to specify the graph g.

Details and Options

Examples

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Basic Examples  (3)

Find the out-component graph of a vertex:

Wolfram Language code: g = [image];
Wolfram Language code: VertexOutComponentGraph[g, {4}]

Highlight the out-component graph of a vertex:

Wolfram Language code: HighlightGraph[g, %]

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

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

Highlight the out-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], VertexOutComponentGraph[g, {7}, i]}], {i, 3}]

Scope  (9)

VertexOutComponentGraph works with undirected graphs:

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

Directed graphs:

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

Multigraphs:

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

Mixed graphs:

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

Tagged graphs:

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

Use rules to specify the graph:

Wolfram Language code: VertexOutComponentGraph[{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: VertexOutComponentGraph[[image], _ ? EvenQ]

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

Wolfram Language code: VertexOutComponentGraph[[image], 1, 2]

VertexOutComponentGraph works with large graphs:

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

Applications  (1)

Build a graph by states that can be reached from 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 be reached from state 4:

Wolfram Language code: VertexOutComponentGraph[g, 4]

Properties & Relations  (1)

Use VertexOutComponent to find the out-component graph:

Wolfram Language code: g = [image];
Wolfram Language code: VertexOutComponent[g, {5}]
Wolfram Language code: Subgraph[g, %]
Wolfram Language code: VertexOutComponentGraph[g, {5}]
Wolfram Research (2021), VertexOutComponentGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/VertexOutComponentGraph.html.

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_vertexoutcomponentgraph, author="Wolfram Research", title="{VertexOutComponentGraph}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/VertexOutComponentGraph.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_vertexoutcomponentgraph, organization={Wolfram Research}, title={VertexOutComponentGraph}, year={2021}, url={https://reference.wolfram.com/language/ref/VertexOutComponentGraph.html}, note=[Accessed: 13-June-2026]}