—In this paper, we conduct extensive simulations to understand the properties of the overlay generated by BitTorrent. We start by analyzing how the overlay properties impact the efficiency of BitTorrent. We focus on the average peer set size (i.e., average number of neighbors), the time for a peer to reach its maximum peer set size, and the diameter of the overlay. In particular, we show that the later a peer arrives in a torrent, the longer it takes to reach its maximum peer set size. Then, we evaluate the impact of the maximum peer set size, the maximum number of outgoing connections per peer, and the number of NATed peers on the overlay properties. We show that BitTorrent generates a robust overlay, but that this overlay is not a random graph. In particular, the connectivity of a peer to its neighbors depends on its arriving order in the torrent. We also show that a large number of NATed peers significantly compromise the robustness of the overlay to attacks. Finally, we evaluat...