how to construct a circulant graph ?

how to construct a circulant graph ?

Answer 1

[Gautam]

Hello Anelmad,

You can plot a circulant graph by creating an adjacency matrix to mention the nodes and connections between the nodes and using the “gplot” function plot the graph. The code below follows this to obtain the corresponding plot

% Define the number of vertices 
n = 16; 
v = [1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0]; % Define the first row with the connections 
C = toeplitz([v(1) fliplr(v(2:end))], v); % Create the circulant matrix 
C = [C, ones(n, 1); ones(1, n), 0]; % Add a row and column for the central vertex 
% Define the coordinates for the vertices 
theta = linspace(0, 2*pi, n+1); 
x = cos(theta(1:end-1)); 
y = sin(theta(1:end-1)); 
coords = [x' y'; 0 0]; 
% Plot the graph 
gplot(C, coords, '-o'); 
axis equal; 
title('Circulant Graph'); 

I have used the “toeplitz” and “fliplr” functions to create a circulant matrix by defining the first row. I have then defined the coordinates for the vertices and used the “gplot” function is used to finally plot the graph.

You can refer to the following documents to learn more about these functions:

• “toeplitz”: https://www.mathworks.com/help/matlab/ref/toeplitz.html
• “fliplr”: https://www.mathworks.com/help/matlab/ref/fliplr.html
• “gplot”: https://www.mathworks.com/help/matlab/ref/gplot.html