Lazy web query…

I’m looking for work about how members of a network build models of the network. In particular how do members of power-law distributed networks build their model of the network around them. For example if a member can sample the network randomly how long does it take for him to form an accurate model? What if his ablity to sample is limited the further he moves away from his home base in the network? My intuition says that the models built using either of these methods are amazingly poor; but I’m curious to read something that talks about this question more formally.