trying to calculate the returnability of a network after every iteration

i have a network which i am doing multiple calculations for. however the main one is the returnabilty using ths formula,

returnability = (trace(expm(AT))-n)/(trace(expm(A))-n);

however with my network, i have removed every edge and added them back randomly using this coding,

AT = triu(A);
m = numedges(G);
n = numnodes(G);
[i,j]=find(AT);
p = randperm(m);
for k = 1:m
I = j(p(k));
J = i(p(k)); 
AT(I,J) = 1;
end

where A is the adjacency matrix for the network.

The main thing i am struggling with is after each iteration of an edge being added i want to calculate the returnability. i know i will need a loop but i am not sure how to code it up.

any help/advice would be appreciated a lot.

Answer 1

[Zinea]

Hi Nicolle Small,

You want to calculate the returnability using the given formula after each iteration of edge addition to the graph. For this, you need to incorporate 2 specific changes in your code:

1. Initialize a vector to store returnability values for each iteration. Add this line at the before the start of the loop.

returnability_values = zeros(m, 1);   

2. Calculate the returnability for this iteration. Add this line just before the ‘end’ statement.

returnability = (trace(expm(AT)) - n) / (trace(expm(A)) - n);  
returnability_values(edge_index) = returnability; 
 

The vector ‘returnabillity_values’ contains the returnability after each iteration.