1. %csv file containing edges and weights
e = csvread('edge.csv');
%finds number of edges
ne = length(e);
%makes sure vertices are in order
for i = 1:ne
if e(i,1) > e(i,2)
A = e(i,1);
e(i,1) = e(i,2);
e(i,2) = A;
e(i,3) = -e(i,3);
end
end
%creates vertex matrix
%finds number of vertices
nv = max(max([e(:,1), e(:,2)]));
V = zeros(1,nv);
for i = 1:ne
A = e(i,1);
B = e(i,2);
V(A) = V(A)+1;
V(B) = V(B)+1;
end
valence = max(V);
V = zeros(1,nv);
v = zeros(nv,valence);
for i = 1:ne
A = e(i,1);
B = e(i,2);
V(A) = V(A)+1;
V(B) = V(B)+1;
v(A,V(A)) = i;
v(B,V(B)) = i;
end
w = e(:,3);
%calculates edge weight
%w = zeros(ne,1);
%for p = 1:ne
% sum = 0;
% for i = 1:ne
% if e(i,1) == p || e(i,2) == p
% if e(i,1) == p
% sum = sum + e(i,3);
% end
% if e(i,2) == p
% sum = sum - e(i,3);
% end

2. % w(p,1) = sum;
% end
% end
%end
% Creates face matrix by searcing for shared edges of a triangle.
% Faces are stored as triples of vertices.
nf = 0;
for i = 1:ne
A = e(i,1); %end points of the selected min edge
B = e(i,2); %end points of the selected min edge
for j = v(A,:) %Edge number search
for k = v(B,:) %Edge number search
if j > i && k > i %-------------------
if e(j,1) == A % This area determines the 'other'
va = e(j,2); % vertex for each edge (j and k)
else % The goal is that these two match.
va = e(j,1); %
end %
if e(k,1) == B %
vb = e(k,2); %
else %
vb = e(k,1); %
end %-------------------
if va == vb && va ~= A && va ~= B %----------------
nf = nf +1; % This area checks
v1 = min([A,B,va]); % that the verts
v3 = max([A,B,va]); % are appropriate
for vert = [A,B,va] % then adds them
if v1 ~= vert && v3 ~= vert % to the faces
v2 = vert; % in the correct
end % orientation.
end %
f(nf,1) = v1; %
f(nf,2) = v2; %
f(nf,3) = v3; %
end %----------------
end
end
end
end
%initialize delta_0 and delta_1
delta_0 = zeros(ne,nv);
delta_1 = zeros(nf,ne);
temp = zeros(1,2);
%creates delta_0
%recall that delta_0(f)[v_1,v_2] = f(v_2) - f(v_1)
for i = 1:ne
delta_0(i,e(i,1))=-1;
delta_0(i,e(i,2))=1;
end
delta_0 = delta_0';

3. delta_0f = delta_0*w;
%creates delta_1
%recall that delta_1(f)[v_1,v_2,v_3] = f(v_2,v_3) - f(v_1,v_3) + f(v_1,v_2)
for i = 1:nf
%Computes f(v_2,v_3)
temp(1,1) = f(i,2);
temp(1,2) = f(i,3);
%Finds the corresponding edge
for k = 1:ne
if temp(1,1) == e(k,1)
if temp(1,2) == e(k,2)
j = k;
end
else
k=k+1;
end
end
delta_1(i,j) = 1;
%Computes f(v_1,v_3)
temp(1,1) = f(i,1);
temp(1,2) = f(i,3);
%Finds corresponding edge
for k = 1:ne
if temp(1,1) == e(k,1)
if temp(1,2) == e(k,2)
j = k;
end
else
k=k+1;
end
end
%-1 because ...-f(v_1,v_3)+...
delta_1(i,j) = -1;
%Computes f(v_1,v_2)
temp(1,1) = f(i,1);
temp(1,2) = f(i,2);
%Finds corresponding edge
for k = 1:ne
if temp(1,1) == e(k,1)
if temp(1,2) == e(k,2)
j = k;
end
else
k=k+1;
end
end
delta_1(i,j) = 1;
end
delta_1 = delta_1';
lap_0 = delta_0'*delta_0;
ONB = null(lap_0);

4. temp = size(ONB);
N = temp(2);
imvec = zeros(1,ne);
for i = 1:N
ort = ONB(:,i);
imvec = imvec + (w'*ort)*ort';
end
ee = zeros(ne,3);
for i = 1:ne %-------------------
ee(i,1) = e(i,1); % Assigns a new
ee(i,2) = e(i,2); % edge flow in
ee(i,3) = imvec(i); % Ker(Lapl).
end %-------------------
csvwrite('loops.csv',ee);
%display(imvec)
%display(w')