You can use `ST_ClosestPoint()` to find the closest one to each point. If you use that in combination with make line you should be able to achieve what you need. Here is a [link to the documentation for ST_ClosestPoint()][1].

You could do it like this -

    select st_asgeojson(st_makeline(g)) from 

        (select geometry as g from testing group by geometry order by st_closestpoint(geometry, geometry)) as f


  [1]: http://www.postgis.org/docs/ST_ClosestPoint.html