This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 GRAPH UTILITIES PACKAGE SYMBOL

# MaximalIndependentEdgeSet

 MaximalIndepndentEdgeSet[g]gives a maximal independent edge set of an undirected graph g.
• gives an approximate maximal set of pairwise nonadjacent edges of g.
• A maximal independent edge set of a graph is also called a maximal matching.
• The following option can be given:
 Weighted False whether edges with higher weights are preferred when forming the maximal independent edge set
This defines a small graph:
This shows that the maximal independent edge set contains three edges:
This plots the hexagon with maximal edges highlighted in red:
Needs["GraphUtilities`"]
This defines a small graph:
 Out[3]=
This shows that the maximal independent edge set contains three edges:
 Out[4]=
This plots the hexagon with maximal edges highlighted in red:
 Out[5]=
 Options   (1)
A matrix representation of a hexagon with a higher weight given to the edge connecting vertices 1 and 6:
This shows that with the default option Weighted->False, the weights are ignored:
This shows that the option Weighted->True, the higher weight edge is included:
 Applications   (1)
This is a matrix representation of the graph of a torus:
This finds the maximal independent edge set of the torus:
This plots the torus, highlighting members of the maximal independent edge set in red: