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}\...
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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 ...
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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 ...
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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 ...