% A  B  C
A = [1 -1 ; %  A B 10
     1 -1 ; %  A B 30
     0  1]; %  B C 50
 
 C = diag(1./[10 30 50]);
 f = zeros(size(A, 2), 1);
 f(1) = 1;
 
 x = A'*C*A\f;
 disp(x(1));
 
 %    A  B  C  D  E  F
 A = [1  0 -1  0  0;  % A C 5
      1 -1  0  0  0;  % A B 10
     -1  0  0  1  0;  % D A 5
      0  0  0  1 -1;  % D E 10
      0  0  1  0 -1;  % C E 10
      0  0  0  0  1;  % E F 15
      0  1  0  0  0]; % B F 20
 
 C = diag(1./[5 10 5 10 10 15 20]);
 f = zeros(size(A, 2), 1);
 f(1) = 1;
 
 x = A'*C*A\f;
 disp(x(1));
 
 %    A  B  C  D
 A = [1 -1  0  ;  % A B 10
      1  0 -1  ;  % A C 10
      0  1  0  ;  % B D 10
      0  0  1  ;  % C D 10
      0  1 -1 ];  % B C 10
 
 
 C = diag(1./[10 10 10 10 10]);
 f = zeros(size(A, 2), 1);
 f(1) = 1;
 
 x = A'*C*A\f;
 disp(x(1));  
 
 

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