In this paper, we formulate a novel question on maximum flow queries. Specifically, this
problem aims to find which k edges would have the largest impact on a maximum flow query
on a network. This problem has important applications in areas like social network and
network planning. We show the inapproximability of the problems and present our heuristic
algorithms. Experimental evaluations are carried out on real datasets and results show that
our algorithms are scalable and return high quality solutions.