Question

I have written a code in MATLAB that allows me to generate a random graph of n vertices, each with c fixed neighbours without loops (note the edges are directed, thus “a connected to b” does not imply “b connected to a”).

However, it is terribly inefficient, especially when I need to it work on magnitudes such as n = 10000 and c = 1000. I was wondering if anyone could optimize it big time, or suggest anything constructive?

function [M]=matsrand(n,c)


MM=0;   %arbitrary starting value
while MM ~=n*c

    M = sparse(zeros(n));       
    ctin = zeros(1,n);  


    for i=1:n
        rp = randperm(n);   %generate vector of the randomly permuted order of n vertices
        rp(rp==i)=[];       %get rid of itself to avoid self connection

        noconnect=find(ctin(:)>=c); %generate list that i is not allowed to connect to
        where=ismember(rp,noconnect);   %returns 1 to the subset noconnect in rp
        noconnectind=find(where);

        rp(noconnectind(:))=[];         %remove the neurons i is not allowed to connect to

        if length(rp)<c
            break
        else
            r=rp(1:c);
        end
        M(i,r)=1;
        ctin(r)=ctin(r)+1;

    end
    MM=sum(ctin);
end

Answer 1

This’ll speed up things a bit:

function [M]=matsrand(n,c)

    MM=0;   %arbitrary starting value
    all_nums=1:n;

    while MM ~=n*c

        M = sparse([],[],[],n,n,n*c);
        ctin = zeros(1,n);

        for ii=1:n
            noconnect=ctin>=c;
            noconnect(ii)=true;

            rem_nums = all_nums(~noconnect); % remaining numbers
            rp=randperm(n-sum(noconnect));
            rp = rem_nums(rp); % remaining numbers, hussled

            if numel(rp)<c
                break
            else
                r=rp(1:c);
            end
            M(ii,r)=1;
            ctin(r)=ctin(r)+1;
        end
        MM=sum(ctin);
    end
end

If memory isn’t an issue, I think you can replace the sparse matrix with an ordinary zeros(n,n).

Main problem still is you have to hit that lucky combination.