What if PageRank didn’t exist?

The guy seems to be thinking too much like a mathematician. The whole purpose of PageRank is not to calculate a perfect mathematical score based on graph topology, it's to model the likely behavior of people surfing the web. Links in the graph represents the flow of attention from one page to the next.

Most of the time people will follow links. But they'll also close pages and open new ones from bookmarks, search engines or memory.

As such, the fact that the PageRank graph is not completely connected doesn't matter, because it's already a subset of the "true" page-to-page graph anyway.

The regularization isn't just a hack to make the numbers work, it also models the uncertainty in user behavior.

Interesting article, except for the fact that you can't read any of the formulas because his LaTeX plugin is broken.

Nothing would change. Seriously, who cares about PageRank?