Mathematica 9 is now available
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.
Wolfram Mathematica Documentation Center
DOCUMENTATION CENTER SEARCH
New to Mathematica? Find your learning path »
Mathematica > Mathematics and Algorithms > Graphs & Networks > Graph Operations and Modifications > GraphComplement >
Mathematica > Visualization and Graphics > Graphs & Networks > Graph Operations and Modifications > GraphComplement >
Mathematica > Mathematics and Algorithms > Graphs & Networks > Constructing Graphs > Graph Operations and Modifications > GraphComplement >
BUILT-IN MATHEMATICA SYMBOLSee Also »|More About »

GraphComplement

GraphComplement[g]
gives the graph complement of the graph g.
MORE INFORMATION
  • The graph complement has the same vertices and edges defined by two vertices being adjacent only if they are not adjacent in g.
EXAMPLESCLOSE ALL
Basic Examples   (2)
Graph complement of cycle graphs:
Graph complement of directed graphs:
Graph complement of cycle graphs:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
 
Graph complement of directed graphs:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
Scope   (3)
GraphComplement works with undirected graphs:
Directed graphs:
Works with large graphs:
Properties & Relations   (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
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team
Format:   HTML  |  CDF