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

# 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.
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]=
 Scope   (3)
GraphComplement works with undirected graphs:
Directed graphs:
Works with large graphs:
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