  There has been a considerable amount of interest in recent years on the
robustness of networks to failures. Many previous studies have concentrated on
the effects of node and edge removals on the connectivity structure of a static
network; the networks are considered to be static in the sense that no
compensatory measures are allowed for recovery of the original structure. Real
world networks such as the world wide web, however, are not static and
experience a considerable amount of turnover, where nodes and edges are both
added and deleted. Considering degree-based node removals, we examine the
possibility of preserving networks from these types of disruptions. We recover
the original degree distribution by allowing the network to react to the attack
by introducing new nodes and attaching their edges via specially tailored
schemes. We focus particularly on the case of non-uniform failures, a subject
that has received little attention in the context of evolving networks. Using a
combination of analytical techniques and numerical simulations, we demonstrate
how to preserve the exact degree distribution of the studied networks from
various forms of attack.
