Network adjacency matrix for connecting n node with probability p

5 次查看（过去 30 天）
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.

请先登录，再进行评论。

请先登录，再回答此问题。

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

请先登录，再进行评论。

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

类别

在 Help Center 和 File Exchange 中查找有关 Creating and Concatenating Matrices 的更多信息

标签

产品


版本

R2021a

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by