Questions tagged [page-rank]
For questions about Google PageRank algorithm and other similar algorithms.
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Page rank of an infinite binary tree
I found this problem in the Mining of Massive Datasets textbook by Jeff Ullman. I tried solving it by doing it recursively, but it seems my answer is wrong. Is there a solution to this problem where ...
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Expression of the stationary distribution of a Markov Chain (PageRank)
I want to find the expression for the PageRank of a webpage defined as in the original paper of Sergey and Larry (The Anatomy of a Large-Scale Hypertextual Web Search Engine).
Consider a directed ...
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Formula like Elo rating but for games where the outcome is numeric?
I'm working on a problem that involves ranking based on pairwise comparisons (it's for a scientific problem, not actually for games). My comparisons return a numerical score (in practice roughly ...
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Does there exist a graph that the page ranks of each node are distinct?
Suppose that there is a graph of $n$ nodes ($n>3$), is it possible that every node has a distinct page rank value?
the page rank is defined as $R$ while $MR=R$, $M$ is the transition matrix.
I have ...
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Personalized PageRank and Random Walks
I have two questions, each regarding personalized PageRank as provided in a paper I'm reading ("Approximate Personalized PageRank on Dynamic Graphs" by Zhang, Lofgren and Goel; see 1, 2, or ...
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Does PageRank imply that eigenvalue one exists for any matrix?
I learned from this lecture that for the PageRank algorithm the following equation holds:
$$r^{i+1}=L r^{i}$$
I thought when the $r$ vector converges $r^{i+1}=r^{i}$, and hence the equation would ...
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Proof of the equivalence of PageRank and degree centrality in undirected connected graphs
Surprisingly, although this is stated everywhere in literature (usually citing surveys), there seems to be no recent source that explicitly proved this statement (there are, however, sources that ...
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Teletrasporation step in Page Rank
I'm reading some definition of page rank, in particular how page rank work on the web graph.
I'm a little bit confused about the definition of the teletransportation step.
How I understand this phase ...
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What is meant by the term: The matrix is "irreducible"
I came across the application of the Power Method used in determining the largest eigenvalue of a matrix in solving Google's PageRank algorithm and as a summary, the entire problem lies in finding the ...
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When are Eigenvector centrality and PageRank equivalent?
The Eigenvector centrality for a graph $G = (V,E)$ is defined as the eigenvector corresponding to the larges eigenvalue of the adjacency matrix $\mathbf{A}$.
The PageRank is a special case of ...
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Mathematical modelling of flu on an island
Given a flu on an island of 10000 people. Every day 15% of healthy people become infected and have a less illness (not require hospitalization), 12% of healthy people become infected and have a more ...
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Explanation on Google’s PageRank is Webpages as Eigenvectors
Help understand what is the matrix A and the vector x discussed below.
Mathematics for Machine Learning Example 4.9
Google uses the eigenvector corresponding to the maximal eigenvalue of
a matrix A ...
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network pagerank algorithm -- custom initial weights vs personalization
I am working with a graph and I want to compute the pagerank of its nodes. I want to emphasize some nodes more than others (and I use the networkx python package).
I can think of two ways of doing ...
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PageRank of the highest rank page (Directed graph)
Suppose the hyperlink matrix of a directed graph is given as follows:
$$A = \begin{pmatrix}0&0&\frac{1}{3}&\frac{1}{2}&0\\ \:\:\:0&0&0&\frac{1}{2}&\frac{1}{3}\\ \:\:\:0&...
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Proof of PageRank Stability
I was reading though Link Analysis, Eigenvectors and Stability by Ng Et al. I am stuck at the last part of the proof of the stability of the PageRank algorithm.
I do not understand how the ...
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