During recent years, peer-to-peer (P2P) file-sharing systems have evolved in many ways to accommodate growing numbers of participating peers. In particular, new features were introduced to change the properties of the unstructured overlay topology formed by these peers. Despite its importance, little is known about the characteristics of these topologies and their dynamics in modern file-sharing applications.

This paper presents a detailed characterization of P2P overlay topologies and their dynamics, focusing on the modern Gnutella network. Using our parallel P2P crawler, we capture a complete snapshot of the Gnutella network with more than one million peers in just a few minutes. Leveraging more than 18,000 such recent overlay snapshots, we characterize the graph-related properties using individual overlay snapshots and overlay dynamics using hundreds of back-to-back snapshots. We show that snapshots captured by a slow crawler can lead to erroneous conclusions -- such as a power-law degree distribution. Our results reveal that while the Gnutella network has dramatically grown and changed in many ways, it still exhibits the clustering and the short path lengths of a small world network. Furthermore, its overlay topology is highly resilient to random peer departure and even systematic attacks. More interestingly, overlay dynamics lead to an "onion-like" biased connectivity among peers where each peer is more likely connected to peers with higher uptime. Therefore, long-lived peers form a stable core that ensures reachability among peers despite overlay dynamics.