As expected, since the confidence level is determined by the number of times the protocol is executed, not which edges are chosen. Each time you select an edge

As expected, since the confidence level is determined by the number of times the protocol is executed, not which edges are chosen. Each time you select an edge you are opening a brand new commitment to the (claimed) coloring of the graph, so even if you choose the same edge every time you are actually checking different commitments.