Skip to content

Instantly share code, notes, and snippets.

Embed
What would you like to do?
Find all the elementary circuits of a directed graph
function [numcycles,cycles] = find_elem_circuits(A)
if ~issparse(A)
A = sparse(A);
end
n = size(A,1);
Blist = cell(n,1);
blocked = false(1,n);
s = 1;
cycles = {};
stack=[];
function unblock(u)
blocked(u) = false;
for w=Blist{u}
if blocked(w)
unblock(w)
end
end
Blist{u} = [];
end
function f = circuit(v, s, C)
f = false;
stack(end+1) = v;
blocked(v) = true;
for w=find(C(v,:))
if w == s
cycles{end+1} = [stack s];
f = true;
elseif ~blocked(w)
if circuit(w, s, C)
f = true;
end
end
end
if f
unblock(v)
else
for w = find(C(v,:))
if ~ismember(v, Blist{w})
Bnode = Blist{w};
Blist{w} = [Bnode v];
end
end
end
stack(end) = [];
end
while s < n
% Subgraph of G induced by {s, s+1, ..., n}
F = A;
F(1:s-1,:) = 0;
F(:,1:s-1) = 0;
% components computes the strongly connected components of
% a graph. This function is implemented in Matlab BGL
% http://dgleich.github.com/matlab-bgl/
[ci, sizec] = components(F);
if any(sizec >= 2)
cycle_components = find(sizec >= 2);
least_node = find(ismember(ci, cycle_components),1);
comp_nodes = find(ci == ci(least_node));
Ak = sparse(n,n);
Ak(comp_nodes,comp_nodes) = F(comp_nodes,comp_nodes);
s = comp_nodes(1);
blocked(comp_nodes) = false;
Blist(comp_nodes) = cell(length(comp_nodes),1);
circuit(s, s, Ak);
s = s + 1;
else
break;
end
end
numcycles = length(cycles);
end
@shafiul

This comment has been minimized.

Copy link

@shafiul shafiul commented Mar 28, 2017

Can you explain how to use the function? Is A an adjacency-matrix representation of the graph?

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment