Restricting movement along edges

Got a feeling this has been posted before but I can’t find it with a forum search…

Is there any way to restrict movement of verticies so they only move along the edges they’re attatched to ? If so how ?

Well, for there to be an edge there would have to be another vertex attached to make the edge, so snap the cursor to the connected vertex that you want to move the first vertex towards (along the edge). Change the ‘scale/rotate with respect to’ icon to cursor (or press the [ . ] period button on your main keyboard keys. Then select the first vertex and scale [s] away.

Example:

Default plane, front view, move one vertex up a grid unit,
Snap the cursor to the moved vertex, Shift_s -> Cursor to Selection,
rotate the view a bit, and then select a vertex at the “bottom of the ramp” created when you moved the first vertex up,
back to front view
press the [ . ] key
press [s]
you should see the vertex following the edge.

Hope that’s clear enough - or maybe you had something more complicated in mind that you were trying to do?