How to find First Zagreb Entropy using Matlab code?

I have a Graph, and I want to find First Zagreb index and Entropy using Matlab code. Please suggest.

Answer 1

[Rushil]

Hi Imran

From the question, I assume that there is a MATLAB “graph” object in use. A typical graph object is used as follows:

s = [1 1 2 3]; % source nodes 
t = [2 3 3 4]; % target nodes 
G = graph(s, t); 

You can read more about the "graph" object here:

https://mathworks.com/help/matlab/ref/graph.html

Now, the first zagreb index can be computed by summing over the squares of degrees of all nodes. Also, a common way to calculate entropy is using Shannon entropy using the degrees of the nodes. Below is the implementation of the same:

degrees = degree(G); 
firstZagrebIndex = sum(degrees.^2);
degreeCounts = histcounts(degrees, 'Normalization', 'probability'); 
entropy = -sum(degreeCounts .* log2(degreeCounts + eps)); % eps is used to avoid log(0) 

To read more about Shannon entropy you can visit and scroll down on this page to "More About":

https://mathworks.com/help/images/ref/entropy.html

Hope it helps