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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:
WeightedFalsewhether 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:
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This shows that the maximal independent edge set contains three edges:
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This plots the hexagon with maximal edges highlighted in red:
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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:
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: