Drawing lines between nearest neighbor points

Question

I am reading a file with 4 columns (índex and 3 coordinates) and I want to plot spheres at these positions:

data = Import["positions.txt", "Table"];
ballspec = {1.*#1, {#2, #3, #4}} & @@@data[[All, 1 ;; 4]];
plot = Graphics3D[{RGBColor[#3], {Opacity[.7], 
       Sphere[{#2}, .25]}} & @@@ ballspec, Axes -> False];
Show[plot]

but I would also like to add lines connecting the nearest neighbor points, how could I proceed?

Answer 1

Perhaps NearestNeighborGraph?:

NearestNeighborGraph[pts]

Answer 2

You can use Nearest:

pts = RandomReal[1, {100, 2}];
pairs = Transpose[{pts, Nearest[pts, pts, 2][[All, 2]]}];
Graphics[{Point[pts], Line[pairs]}]

or in 3D

pts = RandomReal[1, {100, 3}];
pairs = Transpose[{pts, Nearest[pts, pts, 2][[All, 2]]}];
Graphics3D[{Point[pts], Line[pairs]}]

or with colours

pts = RandomReal[1, {100, 3}];
colors = RandomReal[1, {100}];
pairs = Transpose[{pts, Nearest[pts, pts, 2][[All, 2]]}];
Graphics3D[{Transpose@{Hue /@ colors, Sphere[#, 0.025] & /@ pts}, 
  AbsoluteThickness[3], Line[pairs]}]