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| HAL : hal-00702462, version 1 |
| arXiv : 1205.6343 |
| DOI : 10.1088/1751-8113/45/40/405101 |
| Fiche détaillée |  Récupérer au format |
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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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| Quantware group Collaboration(s) |
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| (18/09/2012) |
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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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| Domaine | : | Informatique/Recherche d'information Mathématiques/Théorie des nombres Science non linéaire/Dynamique Chaotique Physique/Matière Condensée/Mécanique statistique |
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| Google matrix – integers – primes – directed networks |
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| Lien vers le texte intégral : |
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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 | |
| Contributeur : Dima Shepelyansky | |
| Soumis le : Mercredi 30 Mai 2012, 12:09:56 | |
| Dernière modification le : Lundi 28 Janvier 2013, 14:46:09 | |
