# Questions tagged [page-rank]

26 questions
Filter by
Sorted by
Tagged with
43 views

### 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 ...
42 views

### 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 ...
15 views

### Markov chain with edges described by random variables?

this is my first stack exchange question, would really appreciate patience if I am misusing the forum. I'm modeling a certain network as a (sparsely connected) Markov chain. Every node in the network ...
• 1
74 views

### 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 ...
• 343
66 views

### 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 ...
• 252
7 views

### Optimize rank order survey experiment

What are methods for describing/comparing rank ordering of many items by multiple evaluators, where evaluators might not have the same items they are evaluating? For example: Suppose I have a dog show ...
• 131
52 views

### 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 ...
• 187
1 vote
172 views

### 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 ...
• 235
1 vote
122 views

### 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 ...
• 113
1 vote
33 views

• 163
41 views

### Show that the vector of ones, e, is an eigenvector of the Google matrix transpose

In the Google matrix where $$G=\alpha A+(1-\alpha)\frac{1}{n}ee^T$$ and $e$ is a vector of ones, how do I show that $e$ is the eigenvector of $G^T$ corresponding to the eigenvalue of 1 I need to ...
• 197
143 views

### Show that columns of PageRank matrix sum to 1

Where the matrix A is replaced with $$G=\alpha A+(1-\alpha)\frac{1}{n}ee^T$$ Is it a sufficient condition a matrix is stochastic if the largest eigenvalue is 1? Or that in this case since A is ...
• 197
1 vote
117 views

### Calculating PageRank of a Google Matrix

Let $A$ the adjacency matrix of a Web Digraph, with $\{0,1\}$ entries. For sake of clarity, we assume that the matrix is irreducible and without full-zero rows (i.e. no leaf nodes in the graph) . ...
1 vote
373 views

### Perron Frobenius Theorem modified

On this site I found a modified version of Perron Frobenius Theorem Perron-Frobenius Theorem: If M is a positive, column stochastic matrix, then: 1 is an eigenvalue of multiplicity one. 1 is ...
• 15
1 vote
106 views

### Connections between the randomness of the normal distribution and Textrank?

In a TED speech on 8:40 the mathematician said that: This algorithm uses the laws of mathematical randomness to determine automatically the most relevant web pages, in the same way as we used ...
• 577
1 vote
22 views

### What is the relationship between the fluid in PageRank and web traffic?

PageRank can be interpreted as the amount of an imaginary fluid that collects at different nodes in a web graph. I would like to know what the relationship is between this imaginary fluid and actual ...
• 1,319
59 views

### Ranking participants based on tiers and totals

I am trying to rank participants based on sets of data that I have. The data used is for a competition. In this competition, you can participate in X amount of events, at the end of the event you ...
• 33
441 views

### Prove that the dimension of the eigenspace corresponding to the eigenvalue $\lambda=1$ of $H$ is at least the number of the clusters..

There are lots of ’islands’ in the world-wide-web, meaning clusters of websites that are not connected to other parts of the world wide web via hyperlinks. Let $H$ denote the column stochastic ...
• 1,370
So, I was trying to model the PageRank algorithm based on the information of an article, and it said that in order to implement the power method, I needed the distribution of the process given by \...