Bill Slawski posted on his blog about the update PageRank patent that was granted today, you can read the full one named Producing a ranking for pages using distances in a web-link graph.
Bill originally covered it when it was filed back in 2015. Bill is known for going through these patents in detail and dumbing it down for the rest of us. It is a very tedious task and if you like that stuff, you can read through it yourself.
Should SEOs freak out and read through this? Will it make a difference in their rankings? The short answer is no.
Although Google still does use PageRank for ranking, they did kill toolbar PageRank numbers years ago to force SEOs and webmasters not to focus on this number.
It is more important to focus on building out content and pages that people want to read, share and link to. Focusing on a PageRank patent, although can be fun, is not always something you can directly control, espesially without being able to see any form of figure from Google on it.
Timely, John Mueller commented on Reddit about the PageRank patent yesterday, when a student was tasked to look at the patent and come up with a web page that gets scored with PageRank. John said:
You can pick a dampening factor and iteratively calculate the theoretical values based on the papers, but it has nothing to do with what happens within Google. It's a fun exercise, if you like a little bit of math but usually you'd use many more pages to make it interesting (eg a smaller language version of Wikipedia).
John said you can "calculate the theoretical values based on the papers" and added "but it has nothing to do with what happens within Google."
Google has said time and time again that just because Google has a patent, it doesn't mean they use it today the way it was written or at all.
Forum discussion at Reddit.