I would like to create a random adjacency matrix in MATLAB such that the total sum of weight is equal to the number of edges. Finally find the Laplacian matrix using
L = diag(sum(A)) - A
and then graph it. Is there any way to do so? Thanks in advance.
An adjacency matrix for an undirected graph is simply a square symmetric matrix.
If you have no constraints on the degree of the nodes only on the weights than I would suggest something like
n ; % number of nodes in the graph
density = 1e-3; % a rough estimate of the amount of edges
A = sprand( n, n, density ); % generate adjacency matrix at random
% normalize weights to sum to num of edges
A = tril( A, -1 );
A = spfun( @(x) x./nnz(A), A );
% make it symmetric (for undirected graph)
A = A + A.';
I have used in this code: