Guess which one is P2P.
Hint, it's the one on the left.
Unfortunately, most of you probably don't understand that. With all of the recent talk of Call of Duty 4: Modern Warfare 2 (electric boogaloo) many people, not just on this forum, have been whining about its peer to peer system. Sure Modern Warfare doesn't use dedicated servers, and sure, that sucks, but it also doesn't use P2P.
If you look at the above diagrams, you should see that the image on the right has everybody getting their data from one computer, lets call him the host. Ping is the time in milliseconds it takes for you to send and receive data to and from the host. You're not going to have any of that on a P2P network, as there is no host. If you see ping, you aren't using P2P.
If any of you have ever used torrents (yeah, I know you have) even Limewire, you're not dealing with hosts or servers, everybody is sharing what they have, you're getting pieces from multiple seeders, while at the same time giving pieces to leechers. This works for torrents, but I can't imagine how this could possibly work in a real time video game, where information is constantly changing.
I really hope that you read this, because it's annoying as hell reading all of you mixing this up. Think about when people think CPU means computer.
TL;DR, Do not call XBL, PSN, MW2 or anything related to games (other than piracy) P2P.
Really.