  We introduce a general framework, applicable to a broad class of random walks
on networks, that quantifies the response of the mean first-passage time to a
target node to a local perturbation of the network, both in the context of
attacks (damaged link) or strategies of transport enhancement (added link).
This approach enables to determine explicitly the dependence of this response
on geometric parameters (such as the network size and the localization of the
perturbation) and on the intensity of the perturbation. In particular, it is
showed that the relative variation of the MFPT is independent of the network
size, and remains significant in the large size limit. Furthermore, in the case
of non compact exploration of the network, it is found that a targeted
perturbation keeps a substantial impact on transport properties for any
localization of the damaged link.
