  This paper presents an analytical framework to model fault-tolerance in
unstructured peer-to-peer overlays, represented as complex networks. We define
a distributed protocol peers execute for managing the overlay and reacting to
node faults. Based on the protocol, evolution equations are defined and
manipulated by resorting to generating functions. Obtained outcomes provide
insights on the nodes' degree probability distribution. From the study of the
degree distribution, it is possible to estimate other important metrics of the
peer-to-peer overlay, such as the diameter of the network. We study different
networks, characterized by three specific desired degree distributions, i.e.
nets with nodes having a fixed desired degree, random graphs and scale-free
networks. All these networks are assessed via the analytical tool and
simulation as well. Results show that the approach can be factually employed to
dynamically tune the average attachment rate at peers so that they maintain
their own desired degree and, in general, the desired network topology.
