It's a Small World for Random Surfers

TL;DR

This paper establishes logarithmic upper bounds for the diameters of two Webgraph models, confirming the small world phenomenon, and provides tight bounds for the case when the graph is a tree.

Contribution

It proves logarithmic diameter bounds for the random-surfer and PageRank-based Webgraph models, advancing understanding of their small world properties.

Findings

Logarithmic upper bounds for diameters of Webgraph models

Confirmation of small world phenomenon in these models

Tight bounds for tree-structured graphs

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.