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 and Options

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.

This specifies a small graph:

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

MaximalIndependentVertexSet has been superseded by FindIndependentVertexSet:

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