The document describes code to find the largest edge weight in a network. It initializes variables to store the largest edge weight found, the vertex and edge history of the path leading to it. It then iterates through each edge, tracking the highest weight found and updating the vertex and edge histories if a new highest is found. It recursively traces paths from the highest weight edge, updating edge weights as it travels the path and breaks if it finds a loop.

1. %find the largest edge weight
e = csvread('loops.csv');
n = length(e);
TT = 50;
%initialize variables
best = 0; % largest edgeweight
best_v = zeros(1,TT); % vertex history
best_e = zeros(2,TT); % edge history
nv = max(max([e(:,1), e(:,2)]));
V = zeros(1,nv);
for i = 1:n
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:n
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
for i = 1:n
if best < abs(e(i,3))
best = abs(e(i,3));
if e(i,3) > 0
best_v(1) = e(i,1);
best_v(2) = e(i,2);
best_e(1,1) = i;
best_e(2,1) = 1;
else
best_v(1) = e(i,2);
best_v(2) = e(i,1);
best_e(1,1) = i;
best_e(2,1) = -1;
end
end
p(1,1) = best_v(1);
p(2,1) = best_v(2);
end
for q = 2:TT
best = 0;
for i = v(best_v(q),1:valence)
if i ~= 0
if e(i,1) == best_v(q)

2. A = 1;
B = e(i,2);
W = e(i,3);
else
A = -1;
B = e(i,1);
W = -e(i,3);
end
for ii = 1:q
if B == best_v(ii)
W = W*(.96+.01*(q-ii));
break
end
end
if W > best
best = W;
best_v(q+1) = B;
best_e(1,q) = i;
best_e(2,q) = A;
end
end
end
if any(best_v(q+1) == best_v(1:q))
break
end
end
for ii = 1:q
if best_v(q+1) == best_v(ii)
link = ii;
break
end
end
loop = best_v(link:q);
nn = n;
for ii = 1:(q+1-link)
for edge = v(loop(ii),1:valence)
if edge ~= 0
e(edge,:) = 0;
nn = nn - 1;
end
end
end
ee = e;
e = zeros(nn,3);
row = 1;
for ii = 1:n
if ee(ii,1) ~= 0
e(row,:) = ee(ii,:);
row = row + 1;
end

3. end