PageRank and RankBrain both seem to be (complicated) features to the actual core search algorithm, which is some unspecified machine learned model [1].

PageRank, for example, can't be the whole search algorithm since it's not even query-dependent. It would just put the same most authoritative document at the top for every query.

Similiarly, RankBrain doesn't sound like it could be the whole algorithm. It sounds like it is just a text understanding model (which wouldn't know anything about e.g. the global reputation of the document, the popularity of the document, etc.). In fact, the article explicitly confirms this:

>RankBrain has become the third-most important signal contributing to the result of a search query, he said.

I'd guess some kind of composite content quality signal and some kind of composite popularity signal sit at #1 and #2.

[1] - I don't have any insider knowledge about how Google works, but this article suggests that they were getting ready to switch from a hand-tuned model to a machine learned one in 2008: http://anand.typepad.com/datawocky/2008/05/are-human-experts...