A path graph is a connected graph denoted by Pn if it contains n nodes. Nodes are connected in form of a straight line in a path graph. Here we will discuss how networkx module can be used to generate one using its inbuilt path_graph() function.
Properties of Path Graph:
- The number of nodes in a path graph(Pn) is N.
- The number of edges in a path graph(Pn) is N-1.
- The diameter of the path graph(Pn) i.e maximum distance between any pair of vertices is N-1 which is between 1st and last node.
- The chromatic number of Path Graph is 2.
- Nodes are assigned labels from 0 to N-1
- Terminal vertices have degree 1 and every other vertex has degree 2.
- A path graph is a connected graph.
- Path graph contains no cycle in it.
- Although the path graph is connected but the removal of any edge will make it unconnected as no cycle is there in Path Graph.
- It is a Planar Graph.
Functions used
We will use the networkx module for realizing a Path graph. It comes with an inbuilt function networkx.path_graph() and can be illustrated using the networkx.draw() method. This method is straightforward method of creating a desired path graph using appropriate parameters.
Syntax: path_graph(n, create_using=None)
Parameter:
- n: Number of nodes we want in path graph.
- create_using: We can simply pass None or pass nx.DiGraph() as a value to this argument sending nx.Digraph() will lead to creation of a directed path graph.
Approach:
- Import module
- Create path graph object using path_graph() function as mentioned above.
- Pass appropriate parameters to the functions
- Display plot
Program:
Python3
# import required moduleimport networkx as nx# create objectG = nx.path_graph(5, create_using=nx.DiGraph())# illustrate graphnx.draw(G, node_color='green') |
Output:
