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Abstract: PageRank is a ranking of the web pages that measures how often a given webpage is visited by a random surfer on the web graph, for a simple model of websurfing. It seems realistic that PageRank may also have an influence on thebehavior of web surfers. We propose here a simple model taking into account themutual influence between web ranking and web surfing. Our ranking, theT-PageRank, is a nonlinear generalization of the PageRank. It is defined as thelimit, if it exists, of some nonlinear iterates. A positive parameter T, thetemperature, measures the confidence of the web surfer in the web ranking. Weprove that, when the temperature is large enough, the T-PageRank is unique andthe iterates converge globally on the domain. But when the temperature issmall, there may be several T-PageRanks, that may strongly depend on theinitial ranking. Our analysis uses results of nonlinear Perron-Frobeniustheory, Hilbert projective metric and Birkhoff-s coefficient of ergodicity.



Autor: Marianne Akian, Stephane Gaubert, Laure Ninove

Fuente: https://arxiv.org/







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