my understanding is an edge is made from two verts.., deleting one should kill the edge.., (though i have seen the edge remain which was annoying at the time). i always though 3D 101 was a vert is a point in 3D space.., two verts can form an edge, three plus form a plane??

if you form a cube, then cut with the edge loop tool.., you can not delete a vert from the new edge made unless you go to 'delete edge/vert' (whatever the name is) and deleting the vert will delete two edges with it by proxy.