How can I find positive feedback loops from a directed graph?

I have directed graphs. The weights of the edges can either +1 or -1. Now I want to find cycles which are equivalent to positive feedback loop.

There are two kinds of regulation activation and inhibition

----| denotes inhibition

→ denotes activation

If there are two nodes both having ----| links then the cycle will be positive feebback loop. Similarly for three nodes and upto maximum number of nodes. The cycle will be positive feedback if there are all → links or even number of ----| links.

If kindly some one suggest me how to find positive feedback loop from a network it will be very helpful? The result should not be isomorphic.

Thanks in advance

Here I am posting my code of the graph.

s = [1 4 2 5 2 3 4 4 6 5 5 6 7 8];

t = [2 1 3 2 4 6 5 7 5 7 8 9 8 9];

w = [1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 1];

G= digraph(s,t,w);

plot(G,'Layout','force','EdgeLabel',G.Edges.Weight)

Answer 1

[Chunru]

s = [1 4 2 5 2 3 4 4 6 5 5 6 7 8];
t = [2 1 3 2 4 6 5 7 5 7 8 9 8 9];
w = [1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 1];
G= digraph(s,t,w);
plot(G,'Layout','force','EdgeLabel',G.Edges.Weight)

% find all cycles
[cycles, edgecycles] = allcycles(G)

cycles = 3×1 cell array
    {[  1 2 4]}
    {[2 3 6 5]}
    {[  2 4 5]}

edgecycles = 3×1 cell array
    {[   1 3 5]}
    {[2 4 11 8]}
    {[   3 6 8]}

positive_feedback = zeros(length(cycles), 1);
for i=1:length(cycles)
    positive_feadback(i, 1) = prod(G.Edges.Weight(edgecycles{i}));
end
positive_feadback

positive_feadback = 3×1

-1 1 -1