Question

I am trying to create a connectivity matrix for a graph with N nodes. The connectivity rules state that it should have 1000 randomly assigned one way connections (nodes cannot be connected to themselves).

What I want to do is to generate a matrix NxN with mostly zeroes and 1000 ones in random places, but not on the main diagonal.

I really don’t have any ideas on how to achieve this. I thought about generating a matrix of random numbers between 0 and N/1000 and then making those above (N-1)/1000 to be one and the rest 0, but this isn’t very precise (I may get more or less than 1000) and I don’t know what to do about the diagonal.

Answer 1

What about this. Find the indices of non-diagonal elements. Choose some of those at random, and then populate those indices with ones:

nn = 10; % Size of matrix
nr = 20; % number of random connections
ident = eye(nn);       
nd_idx = find(~ident); % Indices of non-diag elements
con = randperm(numel(nd_idx), nr); % Pick random elements
m = zeros(nn);
m( nd_idx(con) ) = 1;