# Questions tagged [pagerank]

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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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### Two different formulations of PageRank

I recently read a paper (requires institutional access) which formulates PageRank as an optimization problem  \min_\mathbf{r} d (\mathbf{I}-\mathbf{A})\mathbf{r}+(1-d)\Vert \mathbf{r}-\mathbf{e}\...
1answer
70 views

### What are the conditions for a graph's adjacency matrix to not have a negative eigenvalue with magnitude>=1?

Say I have a (directed) graph $G$ with an adjacency matrix $A$. For the sake of the question, let's assume it's normalized column-wise (edge weights are normalized so the sum of out-edge weights per ...
0answers
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### How to measure “cyclicity” of a directed weighted graph?

Say you have a weighted directed graph with (potentially) some cycles in it. You want to have some sort of a measure of how "cyclical" this graph is. The requirements are: This measure C=0 on an ...
1answer
88 views

### Difference between $2^{nd}$ order random walk and personalized pagerank

I've been recently working with graph sampling, and I can't seem to find useful explanation of the following two aspects. On one side there are pagerank-based algorithms, which converge to a ...
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462 views

### In personalized page rank, should the page rank vector be initialized uniformly?

In (normal) page rank, the (initial) page rank vector is usually initialized to the uniform distribution. Should I do the same for personalized page rank? I wonder if I should initialize the page ...