Exploring Google PageRank - the Impact of "Distant" Links

This the second little note about playing with the Google PageRank algorithm using this little work-in-progress web app.  The results below should be reproducible with it (or let me know if it's not!).

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

The ranking is A=H=E>D>B>C=F, with values 0.25,0.25,0.25,0.13,0.12,0,0, respectively.

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.