How to create a random adjacency matrix with a changeable degree and number of players using only for-loops, and if-statements?

clear all
clc

d=2
n=10;
A = zeros(n,n);  % Create initial matrix 
for i = 1:n
    for j = 1:n 
        if sum(A(i,:))==d || sum(A(:,i))==d 
           MAKE OTHER ENTRIES IN ROW/COLUMN ZERO AND GO TO NEXT ROW/COLUMN
        elseif i==j
            A(i,j)=0;             % Zero values in the diagonal entries                 
        else
            A(i,j)=round(rand);   % Choosing random 0 and 1 values
            A(j,i)=A(i,j);        % Make A matrix symmetric  
        end  
    end
end

Currently I am working on a code that needs the random creation of an adjacency matrix. As can be seen in the code, I still need some working lines for the definition of the (changeable) degree of the network. If the degree of the network is 2, every row can have a maximum of two 1's. The same applies for the columns since all players in the network have a maximum of 2 neighbors. How can I do this for variable degrees and players in this code without making a whole new script? Preferably only using for-loops and if-statements.

Answer 1

[VINAYAK LUHA]

Hi Thijmen,

I understand that you want to create a random adjacency matrix of degree “d” and dimension nxn. In your present setting the time complexity would be o(n^3) however with slight optimization you can achieve the task in o(n^2).

Here’s how to achieve that -

• Keep two counter arrays to keep count of number of ones in respective rows and columns
• Traverse the lower triangular matrix and set the value of an entry based on some threshold applied on value drawn from uniform probability distribution.
• Make the matrix symmetric
• Update the respective counters for columns and rows.

Here’s the code for your reference-

n=8; 

d=3;  %d should be valid, i.e d<10 

adj =zeros(n,n); 

zcRows =zeros(1,n); 

zcCols =zeros(1,n); 
for i=1:n 
    for j=1:n 
        if(i<j) 
            if(zcRows(i)<d &&zcCols(j)<d) 
                adj(i,j)=(rand()>0.5); 
                adj(j,i)=adj(i,j); 
                
                zcRows(i)=zcRows(i)+adj(i,j); 
                zcCols(j)=zcCols(j)+adj(i,j); 
                
                zcRows(j)=zcRows(j)+adj(j,i); 
                zcCols(i)=zcCols(i)+adj(j,i); 
            end 
        end 
    end 
end 
adj

adj = 8×8

0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0

Regards

Vinayak Luha