### Abstract

PageRank is a popularity measure designed by Google to rank Web pages. Experiments confirm that PageRank values obey a power law with the same exponent as In-Degree values. This paper presents a novel mathematical model that explains this phenomenon. The relation between PageRank and In-Degree is modelled through a stochastic equation, which is inspired by the original definition of PageRank, and is analogous to the well-known distributional identity for the busy period in the $M/G/1$ queue. Further, we employ the theory of regular variation and Tauberian theorems to analytically prove that the tail distributions of PageRank and In-Degree differ only by a multiple factor, for which we derive a closed-form expression. Our analytical results are in good agreement with experimental data.

Original language | English |
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Pages (from-to) | 175-198 |

Number of pages | 24 |

Journal | Internet mathematics |

Volume | 4 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - 2009 |

### Keywords

- Taube-rian theorems
- Power law
- EWI-15650
- MSC-68P10
- MSC-90B15
- MSC-40E05
- METIS-264406
- IR-67788
- In-Degree
- Regular variation
- PageRank
- Stochastic equation

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## Cite this

Litvak, N., Scheinhardt, W. R. W., & Volkovich, Y. (2009). In-Degree and PageRank of web pages: why do they follow similar power laws?

*Internet mathematics*,*4*(2-3), 175-198. https://doi.org/10.1080/15427951.2007.10129293