Planar graphs are graphs that can be drawn on a plane without any intersecting edges. In order to draw them, you have to start from a vertex, draw from edge to edge, and keep track of the faces as the drawing continues. According to Kuratowski, a graph is planar if it does not contain a subgraph that is part of the complete graph on five vertices.

The following is a simple example of a planar graph:

Euler's formula connects a number of vertices, edges, and faces. According to Euler's formula, if a finite and connected planar graph is drawn in the plane without any intersecting edge, and if v represents the number of vertices, e represents the number of edges, and f represents the number of faces, then v − e + f = 2.

Besides Mayavi, NetworkX, and planarity, you can use the gamera package to create and display graphs. However, gamera is only available on Windows. We have a simple example here that uses planarity and NetworkX:

import planarity 
import networkx as nx 

# complete graph of 8 nodes, K8 
G8=nx.complete_graph(8) 

# K8 is not planar 
print(planarity.is_planar(G8)) 

# Will display false because G8 is not planar subgraph 
K=planarity.kuratowski_subgraph(G8) 

# Will display the edges
print(K.edges())

#Will display the graph
nx.draw(G8)

False
[(0, 4), (0, 5), (0, 7), (2, 4), (2, 5), (2, 7), (3, 5), (3, 6), (3, 7), (4, 6)]

This example illustrates that the following complete graph of eight nodes is not planar:

The preceding diagram shows that a planar graph with only eight nodes could look messy, so a graph with more nodes will look more complex.