Best I can come up with is

   {."1 ((] , -. {~ {.@I.@(-. +./"1@e. {:@]))^:(<:@#@[) ,:@{.) edges
1 3 17 18 18 20 20 21 22 14 15 16 23 26 25 13 12 11 11 10 9 7 6 5 4 2

Change {.@I. to {:@I. if you want things in the other order.

-- 
Raul
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