Question

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.

Answer 1

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:

• sprand to generate random sparse matrix.
• spfun to help normalize the edge weights.
• tril to extract only half the matrix.