## Abstract

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.

## Keywords

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

### Acknowledgments

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

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