# 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.

# Examples

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## Basic Examples(3)

Find the out-component graph of a vertex:

Highlight the out-component graph of a vertex:

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

Highlight the out-component graph of a vertex:

## Scope(9)

VertexOutComponentGraph works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

Tagged graphs:

Use rules to specify the graph:

Use patterns to select a subset of vertices:

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

VertexOutComponentGraph works with large graphs:

## 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:

Construct the state transition diagram of a transition matrix:

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

## Properties & Relations(1)

Use VertexOutComponent to find the out-component graph:

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_2024_vertexoutcomponentgraph, author="Wolfram Research", title="{VertexOutComponentGraph}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/VertexOutComponentGraph.html}", note=[Accessed: 11-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_vertexoutcomponentgraph, organization={Wolfram Research}, title={VertexOutComponentGraph}, year={2021}, url={https://reference.wolfram.com/language/ref/VertexOutComponentGraph.html}, note=[Accessed: 11-September-2024 ]}