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Find all the elementary circuits of a directed graph
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| 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 |
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