, Volume 76, Issue 2, pp 344–380 | Cite as

It’s a Small World for Random Surfers

  • Abbas MehrabianEmail author
  • Nick Wormald


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.


Random-surfer Webgraph model PageRank-based selection model Small-world phenomenon Height of random trees Probabilistic analysis Large deviations 



The authors thank the referees for their careful readings of the manuscript and their many useful comments.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada
  2. 2.School of Mathematical SciencesMonash UniversityClaytonAustralia

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