# Universal Emergence of PageRank

@article{Frahm2011UniversalEO, title={Universal Emergence of PageRank}, author={Klaus M. Frahm and Bertrand Georgeot and Dima L. Shepelyansky}, journal={ArXiv}, year={2011}, volume={abs/1105.1062} }

The PageRank algorithm enables to rank the nodes of a network through a specific eigenvector of the Google matrix, using a damping parameter $\alpha \in ]0,1[$. Using extensive numerical simulations of large web networks, with a special accent on British University networks, we determine numerically and analytically the universal features of PageRank vector at its emergence when $\alpha \rightarrow 1$. The whole network can be divided into a core part and a group of invariant subspaces. For…

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## References

SHOWING 1-10 OF 48 REFERENCES

Delocalization transition for the Google matrix

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

It is argued that, for networks with delocalized PageRank, the efficiency of information retrieval by Google-type search is strongly affected since the PageRank values have no clear hierarchical structure in this case.

Jordan Canonical Form of the Google Matrix: A Potential Contribution to the PageRank Computation

- Mathematics
- 2005

We consider the web hyperlink matrix used by Google for computing the PageRank whose form is given by A(c)=[cP +(1-c)E]T, where P is a row stochastic matrix, E is a row stochastic rank one matrix,…

Distribution of PageRank Mass Among Principle Components of the Web

- MathematicsWAW
- 2007

A detailed study of the OUT component reveals the presence of "dead-ends" (small groups of pages linking only to each other) that receive an unfairly high ranking when c is close to one, and argues that this problem can be mitigated by choosing c as small as 1/2.

Probabilistic Relation between In-Degree and PageRank

- Computer Science, MathematicsWAW
- 2006

Using the theory of regular variation and Tauberian theorems, it is proved that the tail distributions of PageRank and In-Degree differ only by a multiplicative constant, for which they derive a closed-form expression.

Using PageRank to Characterize Web Structure

- Computer Science, MathematicsInternet Math.
- 2006

It is suggested that PageRank values on the web follow a power law, and generative models for the web graph are developed that explain this observation and moreover remain faithful to previously studied degree distributions.

PageRank: Functional dependencies

- Computer ScienceTOIS
- 2009

PageRank is an interesting mathematical subject that has inspired research in a number of fields and is likely that in certain areas, for instance selective crawling and inverted index reordering (permuting documents so that more important documents are returned first), PageRank (or one of its many variants) is still very useful.

Diffusion of scientific credits and the ranking of scientists

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

This work takes advantage of the entire Physical Review publication archive to construct authors' networks where weighted edges, as measured from opportunely normalized citation counts, define a proxy for the mechanism of scientific credit transfer.

Google's PageRank and beyond - the science of search engine rankings

- Computer Science
- 2006

Any business seriously interested in improving its rankings in the major search engines can benefit from the clear examples, sample code, and list of resources provided.

Two-dimensional ranking of Wikipedia articles

- Computer ScienceArXiv
- 2010

Using CheiRank and PageRank the authors analyze the properties of two-dimensional ranking of all Wikipedia English articles and show that it gives their reliable classification with rich and nontrivial features.

The Anatomy of a Large-Scale Hypertextual Web Search Engine

- Computer ScienceComput. Networks
- 1998