Years ago when I learned about Google PageRank algorithm, my first reaction was this is not the way it should be done! There should be some proof. This probably just shows that my CS education was too theoretical ;). Years later I have learned that indeed there are some nice tools to argue about the running time of PageRank algorithm. And very recently we were able to give some new parallel (in MPC model) algorithms for computing vanilla PageRank. We improved the number of rounds needed from O(log n) to O(log^2 log n) time. You can hear Solbodan talking out it here:

https://lnkd.in/eT2T3aY. #pagerank

https://www.linkedin.com/posts/piotr-sankowski-80a6875_session-3a-walking-randomly-massively-activity-6696850845469859840-M5LW