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| HAL: hal-00702462, version 1 |
| arXiv: 1205.6343 |
| DOI: 10.1088/1751-8113/45/40/405101 |
| Detailed view |  Export this paper |
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| Journal of Physics A: Mathematical and Theoretical 45 (2012) 405101 |
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| PageRank of integers |
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| Klaus M. Frahm 1A. D. Chepelianskii 2 |
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| For the Quantware group collaboration(s) |
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| (2012-09-18) |
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| We build up a directed network tracing links from a given integer to its divisors and analyze the properties of the Google matrix of this network. The PageRank vector of this matrix is computed numerically and it is shown that its probability is inversely proportional to the PageRank index thus being similar to the Zipf law and the dependence established for the World Wide Web. The spectrum of the Google matrix of integers is characterized by a large gap and a relatively small number of nonzero eigenvalues. A simple semi-analytical expression for the PageRank of integers is derived that allows to find this vector for matrices of billion size. This network provides a new PageRank order of integers. |
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| 1: | Laboratoire de Physique Théorique - IRSAMC (LPT) |
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CNRS : UMR5152 – Université Paul Sabatier [UPS] - Toulouse III |
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| 2: | Cavendish Laboratory |
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University of Cambridge |
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| Information et Chaos Quantiques |
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| Subject | : | Computer Science/Information Retrieval Mathematics/Number Theory Nonlinear Sciences/Chaotic Dynamics Physics/Condensed Matter/Statistical Mechanics |
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| Google matrix – integers – primes – directed networks |
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| Fulltext link: |
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| http://fr.arXiv.org/abs/1205.6343 |
| hal-00702462, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00702462 | |
| oai:hal.archives-ouvertes.fr:hal-00702462 | |
| From: Dima Shepelyansky | |
| Submitted on: Wednesday, 30 May 2012 12:09:56 | |
| Updated on: Monday, 28 January 2013 14:46:09 | |
