  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 evaluate the
impact of peer exchange on the overlay properties, and we show that it
generates a chain-like overlay with a large diameter, which will adversely
impact the efficiency of large torrents.
