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.
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