Do P2P networks have disconnected components?

Can someone please prov开发者_如何学Goide links to any paper/reference that talks about disconnected components in P2P networks?

I have found this paper. It deals with various P2P networks including kademlia which is the basis of bittorent DHT. It defines a probabilistic metric called routability rather than talking about connectivity but I guess the two things are related. (With high routability the graph is probably connected.) From the paper:

... we consider the measure of routability, which is defined as the expected number of routable node pairs divided by the number of possible node pairs among the surviving nodes. ...

One paper calls it the islanding problem, another calls it isolated overlays.