Why is the edge reconstruction conjecture stated with the deck defined as the multi set of graphs formed by deleting one edge? Can someone give an example of two graphs such that the edge deleted subgraph **set** is the same but the **multi set** is different?

edit: for vertex deletion, i can see the counterexample : (n copies of $K_{1,2}$) vs (n-2 copies of $K_{1,2} \cup K_1 \cup K_2$)