1,054 research outputs found
Determining factors behind the PageRank log-log plot
We study the relation between PageRank and other parameters of information
networks such as in-degree, out-degree, and the fraction of dangling nodes. We
model this relation through a stochastic equation inspired by the original
definition of PageRank. Further, we use the theory of regular variation to
prove that PageRank and in-degree follow power laws with the same exponent. The
difference between these two power laws is in a multiple coefficient, which
depends mainly on the fraction of dangling nodes, average in-degree, the power
law exponent, and damping factor. The out-degree distribution has a minor
effect, which we explicitly quantify. Our theoretical predictions show a good
agreement with experimental data on three different samples of the Web
A framework for evaluating statistical dependencies and rank correlations in power law graphs
We analyze dependencies in power law graph data (Web sample, Wikipedia sample and a preferential attachment graph) using statistical inference for multivariate regular variation. To the best of our knowledge, this is the first attempt to apply the well developed theory of regular variation to graph data. The new insights this yields are striking: the three above-mentioned data sets are shown to have a totally different dependence structure between different graph parameters, such as in-degree and PageRank. Based on the proposed methodology, we suggest a new measure for rank correlations. Unlike most known methods, this measure is especially sensitive to rank permutations for topranked nodes. Using this method, we demonstrate that the PageRank ranking is not sensitive to moderate changes in the damping factor
Asymptotic analysis for personalized Web search
Personalized PageRank is used in Web search as an importance measure for Web documents. The goal of this paper is to characterize the tail behavior of the PageRank distribution in the Web and other complex networks characterized by power laws. To this end, we model the PageRank as a solution of a stochastic equation , where 's are distributed as . This equation is inspired by the original definition of the PageRank. In particular, models the number of incoming links of a page, and stays for the user preference. Assuming that or are heavy-tailed, we employ the theory of regular variation to obtain the asymptotic behavior of under quite general assumptions on the involved random variables. Our theoretical predictions show a good agreement with experimental data
PageRank in scale-free random graphs
We analyze the distribution of PageRank on a directed configuration model and
show that as the size of the graph grows to infinity it can be closely
approximated by the PageRank of the root node of an appropriately constructed
tree. This tree approximation is in turn related to the solution of a linear
stochastic fixed point equation that has been thoroughly studied in the recent
literature
Usage Bibliometrics
Scholarly usage data provides unique opportunities to address the known
shortcomings of citation analysis. However, the collection, processing and
analysis of usage data remains an area of active research. This article
provides a review of the state-of-the-art in usage-based informetric, i.e. the
use of usage data to study the scholarly process.Comment: Publisher's PDF (by permission). Publisher web site:
books.infotoday.com/asist/arist44.shtm
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