I am looking for a way to find the nearest point for each point in the same layer using ArcGIS network analyst? I tried using the origin destination matrix and used the same layer for both origins and destinations but I got the nearest point being itself, with a distance of 0 meters and a time of 0 minutes.
did you not specify '2' as the number to find in the number of destinations... it is an optional parameter I know but what you would want in your case Check the help topic for Generate Origin Destination Matrix tool help
