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Unstructured overlays form an important class of peer-to-peer networks, notably when content-based searching is at stake. The construction of these overlays, which is essentially a membership management issue, is crucial. Ideally, the resulting overlays should have low diameter and be resilient to massive node failures, which are both characteristic properties of random graphs. In addition, they should be able to deal with a high node churn (i.e., expect high-frequency membership changes). Inexpensive membership management while retaining random-graph properties is therefore important. In this paper, we describe a novel gossip-based membership management protocol that meets these requirements. Our protocol is shown to construct graphs that have low diameter, low clustering, highly symmetric node degrees, and that are highly resilient to massive node failures. Moreover, we show that the …