# Using PageRank to Characterize Web Structure

@article{Pandurangan2006UsingPT, title={Using PageRank to Characterize Web Structure}, author={Gopal Pandurangan and Prabhakar Raghavan and Eli Upfal}, journal={Internet Mathematics}, year={2006}, volume={3}, pages={1 - 20} }

Recent work on modeling the web graph has dwelt on capturing the degree distributions observed on the web. Pointing out that this represents a heavy reliance on "local" properties of the web graph, we study the distribution of PageRank values on the web. Our measurements suggest that PageRank values on the web follow a power law. We then develop generative models for the web graph that explain this observation and moreover remain faithful to previously studied degree distributions. We analyze…

## 149 Citations

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## References

SHOWING 1-10 OF 37 REFERENCES

The Web as a Graph: Measurements, Models, and Methods

- Computer ScienceCOCOON
- 1999

This paper describes two algorithms that operate on the Web graph, addressing problems from Web search and automatic community discovery, and proposes a new family of random graph models that point to a rich new sub-field of the study of random graphs, and raises questions about the analysis of graph algorithms on the Internet.

A stochastic model for the evolution of the Web

- Computer ScienceComput. Networks
- 2002

The PageRank Citation Ranking : Bringing Order to the Web

- Computer Science, MathematicsWWW 1999
- 1999

This paper describes PageRank, a mathod for rating Web pages objectively and mechanically, effectively measuring the human interest and attention devoted to them, and shows how to efficiently compute PageRank for large numbers of pages.

A random graph model for massive graphs

- Computer Science, MathematicsSTOC '00
- 2000

A random graph model is proposed which is a special case of sparse random graphs with given degree sequences which involves only a small number of parameters, called logsize and log-log growth rate, which capture some universal characteristics of massive graphs.

Self-similarity in the web

- Computer ScienceTOIT
- 2002

An extensive characterization of the graph structure of the Web is presented, with a view to enabling high-performance applications that make use of this structure and to optimized algorithm design for Web-scale data analysis.

Scale-free characteristics of random networks: the topology of the world-wide web

- Computer Science
- 2000

Inferring Web communities from link topology

- Computer ScienceHYPERTEXT '98
- 1998

This investigation shows that although the process by which users of the Web create pages and links is very difficult to understand at a “local” level, it results in a much greater degree of orderly high-level structure than has typically been assumed.

The Diameter of a Scale-Free Random
Graph

- Computer ScienceComb.
- 2004

We consider a random graph process in which vertices are
added to the graph one at a time and joined to a fixed number
m of earlier vertices, where
each earlier vertex is chosen with probability…

Deeper Inside PageRank

- MathematicsInternet Math.
- 2003

A comprehensive survey of all issues associated with PageRank, covering the basic PageRank model, available and recommended solution methods, storage issues, existence, uniqueness, and convergence properties, possible alterations to the basic model, and suggested alternatives to the traditional solution methods.