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Legacy Documentation

Mathematica 8 (2010)

This is documentation for Mathematica 8, which was
based on an earlier version of Wolfram Language.
View current documentation (Version 14.3)

GraphComplement

GraphComplement [g]
gives the graph complement of the graph g.
  • The graph complement has the same vertices and edges defined by two vertices being adjacent only if they are not adjacent in g.
(2)
Graph complement of cycle graphs:
Graph complement of directed graphs:
Graph complement of cycle graphs:
Out[1]=
Out[2]=
Graph complement of directed graphs:
Out[1]=
Out[2]=
(3)
GraphComplement works with undirected graphs:
Directed graphs:
Works with large graphs:
(7)
The complement of a CompleteGraph is an edgeless graph:
The complement of the complement is the original graph (for simple graphs):
The complement of the graph can be obtained from its adjacency matrix:
An independent vertex set of the graph is a clique of its complement graph:
The complement of the line graph of is a Petersen graph:
The graph union of any simple graph and its complement is a complete graph:
The graph intersection of any graph and its complement is an empty graph:
New in 8


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