  The edge-removal problem asks whether the removal of a $\lambda$-capacity
edge from a given network can decrease the communication rate between
source-terminal pairs by more than $\lambda$. In this short manuscript, we
prove that for undirected networks, removing a $\lambda$-capacity edge
decreases the rate by $O(\lambda)$. Through previously known reductive
arguments, here newly applied to undirected networks, our result implies that
the zero-error capacity region of an undirected network equals its
vanishing-error capacity region. Whether it is possible to prove similar
results for directed networks remains an open question.
