How to create random graph of n vertices with c fixed neighbours in MATLAB?

I have written a code in MATLAB that allows me to generate a random graph of n vertices, each with c fixed neighbours without self connections (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?

Thanks!

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

[Matt Fig]

Without loops? I see two loops.

Also, what would be an appropriate input that is fairly quick? I used (5,5) and (10,10) and had to ctrl+c after a couple minutes. I just want to see what the code does before I look at optimizing it, but if I cannot even get it to run a simple example fairly quickly I can't help.... So please tell an input that produces a simple, quick output.

[Vic]

n=c is impossible for the vertices cannot self connect (that was what I meant by 'without loops' - sorry for being imprecise). Anything with c<n would work. A quick example would be n=6,c=2 and the output may be:

       0     1     0     0     1     0
       0     0     1     0     0     1
       0     1     0     0     1     0
       1     0     0     0     0     1
       0     0     1     1     0     0
       1     0     0     1     0     0

[Matt Fig]

Thanks! I see I misread your question. I thought you said that it was slow with n=c=1000, but now I see my mistake.

Answer 1

[Vic]

There is an answer on stack exchange: http://stackoverflow.com/questions/11867266/how-to-create-random-graph-of-n-vertices-with-c-fixed-neighbours-in-matlab

However, even that takes a while to find n=1000, c=100...