How does that work in the real world - do google simply not care, or it's "fair use" somehow?
The patent is only for web search, so other applications dont infringe the patent.
First sentence of the abstract of the patent:
"A method assigns importance ranks to nodes in a linked database, such as any database of documents containing citations, the world wide web or any other hypermedia database."
They'd only care if money gained - PR lost == profit.
Years back, graph dbs bragged about implementing PR in a few lines and ecologists using PR on species.
https://neo4j.com/docs/graph-algorithms/current/algorithms/p...
https://phys.org/news/2009-09-web-page-algorithm-critical-sp...
For example, NetworkX, a popular graph library in Python, implements PageRank. [1]
[1] https://networkx.github.io/documentation/networkx-1.10/refer...