import networkx as nx

import matplotlib.pyplot as plt

# Define the modulus $\text{'}$n$\text{'}($size of the ring Zn$)$

n $=5$

# Create an empty graph

G $=$ nx$.$Graph$()$

# Iterate over all possible combinations of $\text{'}$a$\text{'},\text{'}$b$\text{'},$ and $\text{'}$y$\text{'}$ in Zn

for a in range$(1,$ n$)$:

for b in range$(1,$ n$)$:

for y in range$(1,$ n$)$:

# calculate the left$-$hand side of the equation $($ab$)$

lhs $=($a $*$ b$)\%$ n

# calculate the right$-$hand side of the equation y$($ab$)^2$

rhs $=($y $*($a $*$ b$)**2)\%$ n

# check if the equation holds true and if $\text{'}$a$\text{'}$ and $\text{'}$b$\text{'}$ are different

if lhs $==$ rhs and a $!=$ b:

# Add an edge between $\text{'}$a$\text{'}$ and $\text{'}$b$\text{'}$ if the equation is satisfied by $\text{'}$y$\text{'}-\text{'}$a$\text{'}$ and $\text{'}$a$\text{'}$

G$.$add$\_$edge$($a$,$ b$)$

# Create a layout for the nodes

layout $=$ nx$.$spring$\_$layout$($G$)$

# Draw the graph

nx$.$draw$($G$,$ pos$=$layout, with$\_$labels$=$True, node$\_$size$=300,$ node$\_$color$=$'skyblue', font$\_$size$=10)$

# Display the graph

plt$.$title$($f$\text{'}$Graph for $($ab$)=$ y$($ab$)^2$ in Z$\{$n$\}\text{'})$

plt$.$axis$(\text{'}$off$\text{'})$

plt$.$show$()$

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