Barbell Graph Using Python networkx

Prerequisite: networkx

There are many kinds of definitions of the barbell graphs. The most commonly used one is an n-barbell graph which is a simple graph obtained by connecting two copies of a complete graph with n nodes. In this article, we are going to see how to use a barbell graph using python.

Examples of n-barbell graph:

Example 1:

If N=3 Nodes then the graph will be shown as figures:

Example 2:

If N=4 Nodes then the graph will be shown as figures:

Analysis:

1.Total number of nodes(In n-barbell graph):

The Total number of Nodes = 2*N

2.Total number of edges(In n-barbell graph):

Total number of edges = 2*number of edgesin complete graph + 1
=2*(n*(n-1)/2)+1 = n*(n-1) + 1

Properties:

1. The barbell graph contains cycles in it.
2. The barbell graph is connected every two nodes have a path between them.
3. It has a bridge between 2 complete graphs.
4. Bridge may and may not have nodes in it.

Barbell Graphs using Python:

It is realized in python using the barbell_graph(n, m) function of the networkx library and matplotlib library.

• networkx library  Library in python used for realizing and analyzing different kinds of graphs(data structure) in python. For installation use this command:

pip install networkx

• matplotlib library: Library in python used for realizing and analyzing different kinds of functions in python. For installation use this command:

pip install matplotlib

barbell_graph(n, m): It returns a Barbell Graph with two complete graphs of n nodes which are connected via m node bridge in between.

Approach:

• Import networkx and matplotlib libraries.
• Create a networkx graph object G using nx.barbell_graph(n, m) function as mentioned above.
• Use nx.draw_networkx(G) function to print the graph.

Example 1:

Python

# import module
import networkx as nx
import matplotlib.pyplot as plt

# graph created
res = nx.barbell_graph(4, 2)
nx.draw_networkx(res)

Barbell Graph in Python

Explanation: 

As we passed (4,2) as parameter’s to nx.barbell_graph() function is assigned a graph with 4 node clusters joined by a bridge of 2 nodes. And finally, we got the output as a view of graph G using the draw_networkx(G) function. 

Example 2:

Python3

import networkx as nx
import matplotlib.pyplot as plt

res = nx.barbell_graph(4, 0)
nx.draw_networkx(res)

Output: