1) I think that there is a formula, calculating the cost traveling from X to Y:
1 * the count of circles around the letter at Y
+
1/3 * the count of lines connecting X with Y that don't have dots at the Y's end

2) We start from J and choose cheapest connected letter.
3) We don't use letters we have already been.

Based on these 3 simple rules:

We are at J.
J - K: 0.33
J - I: 0
J - E: 1.33

From I:
I - D: 2.33
I - H: 1.33

From H:
H - C: 1.33
H - G: 0.33

From G:
G - B: 2.66
G - K: 0.66

From K:
K - F: 1.33

From F:
F - B: 2
F - A: 1
F - E: 1.33

From A:
A - B: 3
A - C: 1.66
A - D: 2.66
A - E: 2

We finally move to C

contacts: FireSt@Gmail.com please poke me with the URL on replays.