Many real–world networks show a scale–free degree distribution, a structure that is known to be very stable in case of random failures. Unfortunately, the very same structure makes the network very sensitive against targeted attacks on their high-degree vertices. Under attack it is instead preferrable to have a Poissonor normal degree distribution. The paper adresses the question of whether it is possible to design a network protocol that enables the vertices of a decentralized network to switch its topology according to whether it is attacked or just suffers of random failures. We further require that this protocol is oblivious of the kind of removal scenario, i.e., that is does not contain any kind of attack detection. In this article we show how to design such a protocol that is oblivious, needs only local information, and that is capable of switching between the two structures reasonably fast. The protocol is easy to implement and keeps the average degree in the graph constan...