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Nothing. Everybody freely has copied PageRank already. It has became one of the basic teaching material in graph theory.

For example, NetworkX, a popular graph library in Python, implements PageRank. [1]

[1] https://networkx.github.io/documentation/networkx-1.10/refer...

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How does that work in the real world - do google simply not care, or it's "fair use" somehow?

They'd only care if money gained - PR lost == profit.

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."

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...

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