This talk will discuss the relationship between two ideas in network information theory: edge removal and strong converses. Edge removal properties state that if an edge of small capacity is removed from a network, the capacity region does not change too much. Strong converses state that, for rates outside the capacity region, the probability of error converges to 1. We show that for stationary discrete memoryless networks, particular versions of the edge removal property and the strong converse are equivalent. Namely, the "weak" edge removal property---that the capacity region changes continuously as the capacity of an edge vanishes---is equivalent to the exponentially strong converse---that outside the capacity region, the probability of error goes to 1 exponentially fast. This result is proved using a novel, causal version of the blowing-up lemma. It can be used to derive exponentially strong converses for many problems with only a small variation from traditional weak converse proofs.