nth:{*z{((?,/x@*y)_dvl,/y;*y)}[x]/,,y}          / jamie -> vrabi -> sa
g:,/+:'+(1!;-1!;1!';-1!')@\:1000 -1#!_1e6       / 4-way neighbors of 1k 1k grid
\t nth[g;450000]400                             / 93ms = 400th nearest neighbors from 450000

\

jon harrop's Ocaml solution:

http://www.ffconsultancy.com/products/ocaml_for_scientists/complete/index.html

given a graph, possibly containing cycles:

1. The 0th neighbour of a vertex i is the singleton set {i}.
2. The 1st neighbours of vertex i are given in a look-up table.
3. The nth neighbours of i is the union of the neighbours of the n-1th
   neighbours without the n-1th and n-2th neighbours.

/ simple circular chain, g i = neighbors of i
g:+-1 1!\:!1000

/ recursive nth
{:[z=0;,y;z=1;x i;(?,/x@*t)_dvl,/t:y _f[x]'z-1 2]}
{:[z=0;,y;z=1;x i;{(?,/x y)_dvl y,z}[x]. y _f[x]'z-1 2]}

/ i.e.

join:,
flat:join/
distinct:?:
union:distinct flat@
singleton:,:
without:_dvl
first:*:
at:@

nth:{[g;i;n]
 :[n=0  ;singleton[i]
   n=1  ;at[g;i]
         without[union[at[g;nth[g;i;n-1]]];join[nth[g;i;n-1];nth[g;i;n-2]]]]}

/ q (jamie -> sa)
{first z{((distinct raze x[first y])except raze y;first y)}[x]/enlist enlist y}

/ k w/explicit loop
{r:,,y;do[z;r:((?,/x@*r)_dvl,/r;*r)];*r}

/ 2^nth nearest neighbors of all vertices:
nth_2:{y{(!#x){(,/y)_dv x}'x x}/x}
g:+-1 1!\:!10
  nth_2[g;0]
(9 1
 0 2
 1 3
 2 4
 3 5
 4 6
 5 7
 6 8
 7 9
 8 0)
  nth_2[g;1]
(8 2
 9 3
 0 4
 1 5
 2 6
 3 7
 4 8
 5 9
 6 0
 7 1)
  nth_2[g;2]
(6 4
 7 5
 8 6
 9 7
 0 8
 1 9
 2 0
 3 1
 4 2
 5 3)