finding cycles in directed graph

I am creating a random adjacency matrix for a directed graph and I want to find the cycles. I am using the findcycles function that I found online

I have the following code

rand('seed',1)
n=5;
A=zeros(5);
x=zeros(1,n);
for i=1:n
    A(:,i)=randperm(n);
end
A
adj=zeros(n);
for i=1:n
    adj(i,A(1,i))=1;
end
   view(biograph(adj))
   findcycles(adj)

But I get the following error, any ideas?

Warning: Self connecting nodes are not allowed, ignoring the diagonal of CM. 
> In biograph (line 160)
  In tops (line 13) 
Error: File: findcycles.m Line: 5 Column: 10
Invalid expression. Check for missing multiplication operator, missing or unbalanced delimiters, or other syntax error. To construct matrices, use
brackets instead of parentheses.
Error in tops (line 14)
   findcycles(adj)

[Christine Tobler]

This sounds like there's a bug in findcycles.m (an invalid expression on line 5). Where did you find it?

[Josué Ortega]

Thanks, the problem was solved using sparse(adj).

Then the output looks like

ans =

1 4

ans =

3

My question now is how to save the answers into a variable, say called results. This is a problem because I do not know how many cycles the command is going to find. So something like

[result1, result2] = findcycles(sparse(adj))

will not work because sometimes there is one, sometimes two, sometimes three outputs.

[Christine Tobler]

I can't really help without knowing the definition of the findcycles function.

[Josué Ortega]

function findcycles(G)
numNodes = size(G,1); 
for n = 1:numNodes
   [D,P]=graphtraverse(G,n);
   for d = D
       if G(d,n)
           graphpred2path(P,d)
       end
   end
   G(n,:)=0; 
end

[Christine Tobler]

Here's a way that you can change the function to return all the cycles into a cell array:

function pathCell = findcyclesMod(G)
numNodes = size(G,1); 
pathCell = {};
for n = 1:numNodes
   [D,P]=graphtraverse(G,n);
   for d = D
       if G(d,n)
           pathCell{end+1} = graphpred2path(P,d);
       end
   end
   G(n,:)=0; 
end

A cell array is a datastructure where every element can contain an array of varying size, so each element of pathCell contains a vector that represents one path.

Looking at the findcycles function, it seems this won't find all the cycles. In an example:

Here findcycles returns the following cycles:

     1     5
     1     5     2     3
     2     3     5
     2     3     5     6     4
     3     5     6
     3     5     6     4
     4     6

This is not showing the possible cycle [2 6 4], for example.

Would you mind telling a bit more about what your requirements are for findcycles? Do you need all cycles in a graph, or just a cycle for any node that contains a cycle? Many of the possible cycles can be just recombinations of other existing cycles (for example in a complete graph (a graph where every pair of two nodes is connected by an edge), any list of nodes would be a cycle, leading to a very long list even for small graphs.

[Emanuele Giacomuzzo]

I'm trying to make this code work for myself, but I have problems in running the graphtraverse function. The graph I am working with is - according to MATLAB - a non-sparse one. So the function won't work on it. Is there any function like graphtraverse that works on non-sparse matrices?

The attached file is my non-sparse adjacency matrix.

Cheers!

[Emanuele Giacomuzzo]

Got it! I solved the problem by converting my adjacency matrix using the sparse function.