# Why can two nodes at the same potential be collapsed into one node?

I have a problem where I have a cube with resistance $$R$$ along each edge. I am asked to find the potential between various nodes (corners) using symmetry and the fact that two nodes at the same potential can be collapsed to one point without changing the equivalent resistance between the two given nodes. Using this fact, I think I have solved the problem, and indeed I don't want help with the problem. However, I want to know why this fact holds. If I am drawing a circuit of the cube above, and the potential between, let's say, the upper far corner and all three adjacent corners is the same, why can I depict this as three resistors in parallel between two nodes? (I assume that there are terminals on two of the nodes between which I want to measure the potential).

• If you short-circuit 2 nodes of the same potential, how much current will run through the short-circuit? – Qmechanic Oct 18 at 1:07