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?

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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. ...

_{(source: imagehost.org)}

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