I have an adjacency matrix .Now I want to rewire by replacing two edges at random.I have tried please see below

clc;
clear all;
n = 10;
C= zeros(n, n);
C(1,n)=1;
C(1,n-1)=1;
C(2,n)=1;
A = zeros(n, n);
for i = 1:n
    for j = 1:n
        if j==i+1 || j == i + 2
            A(i,j) = 1;
        else
            A(i, j) = 0;
        end
    end
end
B1=A+C;
B=B1+B1';

##

umEdgesToRewire =2; 
matrixSize=10;
edgesToRewire = randperm(matrixSize, numEdgesToRewire);
for i = 1:numEdgesToRewire
    node1 = edgesToRewire(i);
    node2 = randi([1, matrixSize]);
    
    while node2 == node1 || B(node1, node2) == 1
        node2 = randi([1, matrixSize]);
    end
    
    B(node1, node2) = 1;
    B(node2, node1) = 1;
end

Answer 1

[Tejas]

Hello MKS,

It seems you want to rewire an adjacency matrix by removing two random edges and adding two new ones.

Here are the steps to achieve this:

• Use the 'triu' function to obtain the upper triangular part of the matrix. For more information on 'triu' function, refer to this documentation: https://www.mathworks.com/help/matlab/ref/triu.html .
• Use the 'find' function to locate the indexes of non-zero elements. This will assign indexes to each edge in the adjacency matrix. For more information on 'find' function, refer to this documentation: https://www.mathworks.com/help/matlab/ref/find.html .

    numEdgesToRewire = 2; 
    [existingEdgesRow, existingEdgesCol] = find(triu(B)); 

• Then, use the 'randperm' function to select two edges randomly. More information on this function, is in the documentation: https://www.mathworks.com/help/matlab/ref/randperm.html .

    indicesToRemove = randperm(length(existingEdgesRow), numEdgesToRewire); 

• The following code snippet can be used to remove the selected edges:

    for k = 1:numEdgesToRewire 
        node1 = existingEdgesRow(indicesToRemove(k)); 
        node2 = existingEdgesCol(indicesToRemove(k)); 
        B(node1, node2) = 0; 
        B(node2, node1) = 0; 
        disp(['Removed edge between nodes ' num2str(node1) ' and ' num2str(node2)]); 
    end 

• Use a while loop to find nodes and add new edges, as demonstrated in the code snippet below:

    for k = 1:numEdgesToRewire 
        node1 = randi(n); 
        node2 = randi(n); 
        
        % Check for self-loops or existing edges 
        while node1 == node2 || B(node1, node2) == 1 
            node1 = randi(n); 
            node2 = randi(n); 
        end 
        
        disp(['Adding new edge between nodes ' num2str(node1) ' and ' num2str(node2)]); 
        B(node1, node2) = 1; 
        B(node2, node1) = 1; 
    end