Network adjacency matrix for connecting n node with probability p

i have write this but is not running

clc;
clear all
n=10;
p=0.4;
adj_matrix = generate_adjacency_matrix(n, p)

adj_matrix = 10×10

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

function adj_matrix = generate_adjacency_matrix(n, p)
% Initialize an n x n matrix with all zeros
adj_matrix = zeros(n, n);

% Loop through all possible node pairs
for i = 1:n
    for j = 1:n
        % Skip diagonal elements (no self-loops)
        if i == j
            continue;
        end
        
        % Generate a random number between 0 and 1
        random_number = rand();
        
        % If the random number is less than p, add a link between nodes i and j
        if random_number < p
            adj_matrix(i, j) = 1;
            adj_matrix(j, i) = 1; % Since it's an undirected network
        end
    end
end
end

[Torsten]

Works for me (see above).

But you should only run through the indices above (or below) the main diagonal because it's an undirected graph.

Answer 1

[Torsten]

clc;
clear all
n=10;
p=0.4;
adj_matrix = generate_adjacency_matrix(n, p)

adj_matrix = 10×10

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

(nnz(adj_matrix(:))-n)/(n^2-n)

ans = 0.4222

function adj_matrix = generate_adjacency_matrix(n, p)
% Initialize an n x n matrix with all zeros
adj_matrix = eye(n);

% Loop through all possible node pairs
for i = 1:n-1
    for j = i+1:n       
        % Generate a random number between 0 and 1
        random_number = rand();
        % If the random number is less than p, add a link between nodes i and j
        if random_number < p
            adj_matrix(i, j) = 1;
            adj_matrix(j, i) = 1; % Since it's an undirected network
        end
    end
end
end

[mks]

Thanks a lot.

please give your contact details .

[Torsten]

Seems the matrix always has zeros on the diagonal:

rng("default")
n=10;
p=0.4;
adj_matrix = generate_adjacency_matrix(n, p);
nnz(adj_matrix(:))/(n^2-n)

ans = 0.3556

function adj_matrix = generate_adjacency_matrix(n, p)
% Initialize an n x n matrix with all zeros
adj_matrix = zeros(n);
% Loop through all possible node pairs
for i = 1:n-1
    for j = i+1:n       
        % Generate a random number between 0 and 1
        random_number = rand();
        % If the random number is less than p, add a link between nodes i and j
        if random_number < p
            adj_matrix(i, j) = 1;
            adj_matrix(j, i) = 1; % Since it's an undirected network
        end
    end
end
end

Answer 2

[Bruno Luong]

Method without loop, generate entire matrix, symmetrize then remove self-connexion

p=0.4;
n=10;

A = GenerateAMat(p, n);

A

A = 10×10 logical array
   0   1   0   1   0   0   1   0   0   0
   1   0   1   0   0   0   1   1   1   0
   0   1   0   0   0   0   1   1   0   1
   1   0   0   0   1   1   0   0   0   1
   0   0   0   1   0   0   0   1   1   0
   0   0   0   1   0   0   0   0   0   1
   1   1   1   0   0   0   0   1   1   1
   0   1   1   0   1   0   1   0   1   1
   0   1   0   0   1   0   1   1   0   0
   0   0   1   1   0   1   1   1   0   0

nnz(A)/numel(A)

ans = 0.4200

function A = GenerateAMat(p, n)
A = rand(n) <= 1-sqrt(max(1-p*n/(n-1),0)); 
A = A|A'; 
A(1:n+1:end)=0;
end

Answer 3

[Bruno Luong]

Pretty similar to Torsen's solution. Adjust the density and no-loop

p=0.1;
n=30;

A = GenerateAMat2(p, n);
nnz(A)/numel(A)

ans = 0.1089

function A = GenerateAMat2(p, n)
A = zeros(n);
A(triu(true(n),1)) = rand(1,n*(n-1)/2) <= p*n/(n-1);
A = A+A'; 
end