V     E
v0:{v1,v2}
v1:{v3}
v2:{v3}
v3:{}

V     E
v0: {v1,v2} mark, enqueue v0
v1: {v3}
v2: {v3}
v3: {}

V     E
v0: {v1,v2} dequeue v0;mark, enqueue v1,v2
v1: {v3}
v2: {v3}
v3: {}

V     E
v0: {v1,v2}
v1: {v3} dequeue v1; mark,enqueue v3
v2: {v3}
v3: {}

V     E
v0: {v1,v2}
v1: {v3}
v2: {v3} dequeue v2, check its adjacency list (v3 already marked)
v3: {}

V     E
v0: {v1,v2}
v1: {v3}
v2: {v3}
v3: {} dequeue v3; check its adjacency list

V     E
v0: {v1,v2} |E0|=2
v1: {v3}    |E1|=1
v2: {v3}    |E2|=1
v3: {}      |E3|=0

|V| + |E0| + |E1| + |E2| +|E3| == |V|+|E|
 4  +  2   +  1   +   1  + 0   ==  4 + 4
                           8   ==  8