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I came across a topic on computational linear algebra that talks about iterative algorithms to compute eigenvalues. I've worked with power method which is an iterative algorithm that converges a sequence of vectors to the largest eigenvalue.

One application of power method is the famous PageRank algorithm developed by Larry Page and Sergey Brin. The whole concept of this algorithm is an eigenvector problem corresponding to the largest eigenvalue of a system $Gv=v$ where $G$ is the Google matrix. This eigenvector can be found using the Power method.

Interestingly, I was wondering if PageRank has any application other than web surfing because it combines the concept of random walk and some computational graph theory and linear algebra which I suspect could have some applications in data science. Any idea is welcomed.

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Hubáček et al apply PageRank to football match prediction:

PageRank was originally developed for assessing the importance of a website by examining the importance of other websites referring to it. Similarly, our assumption was that a strong team would be determined by having better results against other strong teams. The PageRank of a team can be computed out of a matrix with columns as well as rows corresponding to teams. Each cell holds a number expressing the relative dominance of one team over the other in terms of previous match outcomes. In particular, the $i, j$ cell contains $$\frac{3w_{ij}+d_{ij}}{g_{ij}}$$ where where $w_{ij} (d_{ij})$ is the number of wins (draws) of team $i$ over (with) team $j$, and the normalizer $g_{ij}$ is the number of games played involving the two teams. These numbers are extracted from the current and the two preceding seasons. The coefficient $3$ reflects the standard soccer point assignment.

The idea is based on PageRank Approach to Ranking National Football Teams by Lazova and Basnarkov.

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