PageRank of integers
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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Mean Field Analysis of Personalized PageRank with Implications for Local Graph Clustering
We analyse a mean-field model of Personalized PageRank on the Erdos-Renyi random graph containing a denser planted Erdos-Renyi subgraph. We investigate the regimes where the values of Personalized PageRank concentrate ar…
ClusteringGraph ClusteringSensitivity of quantum PageRank
In this paper, we discuss the sensitivity of quantum PageRank. By using the finite dimensional perturbation theory, we estimate the change of the quantum PageRank under a small analytical perturbation on the Google matri…
SensitivityLimits of PageRank-based ranking methods in sports data
While PageRank has been extensively used to rank sport tournament participants (teams or individuals), its superiority over simpler ranking methods has been never clearly demonstrated. We use sports results from 18 major…
Fast Incremental and Personalized PageRank
In this paper, we analyze the efficiency of Monte Carlo methods for incremental computation of PageRank, personalized PageRank, and similar random walk based methods (with focus on SALSA), on large-scale dynamically evol…
PageRank Algorithm using Eigenvector Centrality -- New Approach
The purpose of the research is to find a centrality measure that can be used in place of PageRank and to find out the conditions where we can use it in place of PageRank. After analysis and comparison of graphs with a la…