Why isn't 'Loop selection' working if object only has edges? Here are the steps:


Create a cube: SHIFT+A > Mesh > Cube
Enter Edit mode: TAB
Unselect All: A
Go into edge select mode : CTRL+TAB > Edge


At this stage, just a side note: I will not be able to select a loop if I ALT+RMB on any edge... For my understanding, the 4 edges of the top face of the cube are a loop. In the below screenshot, I couldn't select those 4 edges with ALT+RMB.




Add a loop cut: CTRL+R 
Change to face selection: CTRL+TAB >Face 
Select All : A 
Delete all faces (only) : X > Only faces
Change to edge selection: CTRL+TAB > Edge 
Try to select the previously inserted loop with ALT+RMB


=>It will not works... It will select all the edges

My question is: is it possible to select loop on object with no face?
For my understanding, the 4 edges of the top face of the cube are a loop.


Sure, they form a loop... but so do each of the other faces of the cube.

Each corner of the cube is a pole, where the edge flow can fork in either of three directions. So while it may be obvious to you which four edges you want to select, Blender has no way of knowing your intentions.