# graph edges are of the form: (first node) (second node) (weight)
a  b 4  h 8
b  a 4  c 8  h 11
c  b 8  d 7  f 4  i 2
d  c 7  e 9  f 14
e  d 9  f 10 
f  e 10 d 14 c 4  g 2
g  f 2  i 6  h 1
h  g 1  i 7  b 11 a 8
i  c 2  g 6  h 7