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The theory of complex networks provides effective mathematical tools for analyzing properties of communication systems. This paper discusses an approach for modeling fault-tolerance in self-organizing peer-to-peer overlays. The evolution of the network is characterized by resorting to a failure and attachment rate probabilities, together with equations modeling the protocol that peers adopt for the overlay management. Using generating functions, the model is turned into a (partial) differential equation, whose solution provides insights on the nodes' degree probability distribution. Two protocols are considered, which differ in the way peers create links with others. In the first case, peers create novel links based on a pure probabilistic model while, in the second case, they try to maintain a given number of links, during the evolution.
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