Network adjacency matrix for connecting n node with probability p

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mks
mks 2023-7-30
编辑： Bruno Luong 2023-7-30
Ran in:
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
  1 个评论
Torsten
Torsten 2023-7-30
编辑：Torsten 2023-7-30
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.

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回答（3 个）

Torsten
Torsten 2023-7-30
编辑：Torsten 2023-7-30
Ran in:
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
  2 个评论
Torsten
Torsten 2023-7-30
Ran in:
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

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Bruno Luong
Bruno Luong 2023-7-30
编辑：Bruno Luong 2023-7-30
Ran in:
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
Bruno Luong
Bruno Luong 2023-7-30
编辑：Bruno Luong 2023-7-30
Ran in:
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

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