We have 5 nodes. Say E1 joins N1 and N2. E2 joins N2 and N3. Now, it might happen E3 will join E1 and E3. Hence, E3 might not get included. 1 and 2 should be because they will always connect 3 different nodes.
I drew a graph and I guess 8,9,10 will never get included because till you draw 7 edges. All nodes will be connected.
Not sure though