Note that it has been stated that PageRank is now one of over a hundred factors used to rank pages, so it is unclear how much this matters for Google's rankings today.
Here's the before - the sizes of the circles correspond to the calculated PageRank (damping factor 1, but that doesn't seem to affect the results in this case):
|A Little Web - Sizes Correspond to Calculated PageRank|
Now, see what happens to when we connect A to F:
|A Little Web - One Page Adds a Single Link and It Has an Impact on PageRank|
All we did was connect A to F, and yet the impact is surprising. The ranking is now A>B>C=E=F=F>D, with values 0.25,0.19,0.13,0.13,0.13,0.13,0.6, respectively.
What struck me when playing with this was the impact on page D. It is not directly connected to A at all, and yet its PageRank gets cut in half (from 0.13 to 0.06) and moves from 4th to last, all because of something that happened somewhere else. The impact of a "distant" small but abrupt change that, even in the case of a tiny network, is difficult to predict. And what about a network of 42 billion pages?
This Miyoko Shida Rigolo performance seems relevant yet again.