GraphUtilities`
GraphUtilities`

# MaximalIndependentVertexSet

As of Version 10, all the functionality of the GraphUtilities package is built into the Wolfram System. >>

MaximalIndependentVertexSet[g]

gives a maximal independent vertex set of an undirected graph g.

MaximalIndependentVertexSet[g,w]

gives a maximal independent vertex set of g with vertices weighted by w.

# Details

• MaximalIndependentVertexSet functionality is now available in the built-in Wolfram Language function FindIndependentVertexSet.
• To use MaximalIndependentVertexSet, you first need to load the Graph Utilities Package using Needs["GraphUtilities`"].
• MaximalIndependentVertexSet gives an (approximate) maximal set of vertices such that no two vertices form an edge. It treats the input as an undirected graph.
• The length of the vector w must be the same as the number of vertices in g.

# Examples

## Basic Examples(2)

 In[1]:=

This specifies a small graph:

 In[2]:=
 In[3]:=
 Out[3]=

This shows that the maximal independent vertex set contains three vertices:

 In[4]:=
 Out[4]=

MaximalIndependentVertexSet has been superseded by FindIndependentVertexSet:

 In[1]:=
 Out[1]=
 In[2]:=
 Out[2]=