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?

Best I could think of was an $$$O(V(V+E))$$$ approach. If anyone knows any better running time algorithm, do share your approach.

Thanks.