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Wheel Graph using Networkx Python

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  • Last Updated : 17 May, 2021

A wheel graph is a type of graph in which if we connect each node in an n-1 node cycle graph to nth node kept at the centre we get a wheel graph. The definition would be more clear after seeing the example below.

Wheel Graph with n nodes is represented by Wn .

Example:

W5:

W5

 W6:

W6

Properties of Wheel Graph:

  • Total number of edges are 2(N-1)
  • It is a planar graph.
  • The diameter of the wheel graph is 2 if n>4 or 1 if n=4.
  • It is a kind of Hamiltonian Graph.
  • Wheel Graph with n nodes is represented by Wn .
  • It is a cyclic graph.

We will use the networkx module for realizing a Wheel graph. It comes with an inbuilt function networkx.wheel_graph() and can be illustrated using the networkx.draw() method. This module in Python is used for visualizing and analyzing different kinds of graphs.

Syntax:

networkx.wheel_graph(n)

 Parameters:

  • N: Number of nodes in wheel graph.
  • Returns a wheel graph object.

networkx.draw(G, node_size, node_color)

  • Used to realize the graph by passing graph object.
  • G: It refers to the Wheel graph object
  • node_size: It refers to the size of nodes.
  • node_color: It refers to color of the nodes.

Approach:

  • We will import the required module network
  • We will set the number of nodes or n=5.
  • Then we will create a graph object using networkx.wheel_graph(n).
  • For realizing the graph, we will use networkx.draw(G).
  • This will print the required wheel graph.

Implementation:

Python3




# import required module
import networkx
 
# number of nodes
n = 5
 
# create object
G = networkx.wheel_graph(n)
 
# illustrate graph
networkx.draw(G)

Output:

Explanation:

As we initialized n=5 the wheel graph with 5 nodes with a cycle graph having 4 nodes and a central node connected to all other nodes is printed using networkx inbuilt draw function.

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