Visualizing the complement of a graph using networkx

Given a graph G complement of the graph is obtained by removing the edges contained in G from the complete graph having the same number of nodes as G.  

Example:

Initial Graph G:

G

The complement of G:

G Complement

Realizing Complement using Python :

We will use networkx.complement() function for our task

Syntax:

networkx.complement()

• Returns the complement of the graph object passed.
• The value returned is of the same type of the value passed i.e networkx graph object.
• G is the initial object passed.
• Although the complement is being created but no self-loops and parallel edges are created.

Working of complement(G) function:

An edge (n,n2) where n is iterator used to iterate over G is added to complement graph if following conditions are met:

• n and n2 are not neighbours i.e n2 are in the adjacency list of n and vice versa.
• And n != n2.
• n and n2 both are part of G.

Approach:

• We will import networkx with an alias nx.
• Create a sample graph object G using path_graph() function.
• We will then call complement function passing G as an argument.
• We will capture the object returned by complement function in another object G_C.
• We will then call draw() function passing G_C as an argument which will display of the complement graph.

Python3

# importing networkx module
import networkx as nx

# creating sample graph object
G = nx.path_graph(3)

# complement of G and saving in G_C
G_C = nx.complement(G)


# calling draw() to visualize the original graph
nx.draw(G, node_color='Green', with_labels=True)


# calling draw() to visualize the complement graph
nx.draw(G_C, node_color='Green', with_labels=True)

Output:

Original Graph

Complement Graph

By using the complement() method all the edges in G were removed and all other possibilities were added to the complement of G and printed.