I came across this problem in which you have been given a directed graph $$$G=(V,E)$$$ with $$$|V|,|E|\leq 10^5$$$ and one additional edge can be added to $$$E$$$. What can be the maximum size of a strongly connected component in the resulting graph?

If anyone knows an approach, do share.

Thanks.

EDIT: I apologize that the $$$O(V.(V+E))$$$ algorithm that I thought would solve this also turned out to be incorrect.