# 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

open allclose all

## Basic Examples(3)

Find the in-component graph of a vertex:

Highlight the in-component graph of a vertex:

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

Highlight the in-component graph of a vertex:

## Scope(9)

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

VertexInComponentGraph works with large graphs:

## 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:

The most interesting subject of the month:

Show the network generated by this message:

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:

Construct the state transition diagram of a transition matrix:

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

## Properties & Relations(1)

Use VertexInComponent to find the in-component graph: