It's a Small World for Random Surfers
  We prove logarithmic upper bounds for the diameters of the random-surfer Webgraph model and the PageRank-based selection Webgraph model, confirming the small world phenomenon holds for them. In the special case when the generated graph is a tree, we provide close lower and upper bounds for the diameters of both models. 
Abbas Mehrabian and Nick Wormald
cs.DM math.PR