The PageRank algorithm that first set Google on a path to glory measures the importance of a page in the world wide web. It’s fair to say that an entire field of study has grown up around the analysis of its behaviour.

That field looks set for a shake up following the publication today of an entirely new formulation of the problem of ranking web pages. Nicola Perra at the University of Cagliari in Italy and colleagues have discovered that when they re-arrange the terms in the PageRank equation the result is a Schroedinger-like wave equation.

So what, I hear you say, that’s just a gimmick. Perhaps, but the significance is that it immediately allows the entire mathematical machinery of quantum mechanics to be brought to bear on the problem–that’s 80 years of toil and sweat.

Perra and pals point out some of the obvious advantages and disadvantages of the new formulation.

First, every webpage has a quantum-like potential. The topology of this potential gives the spatial distribution of PageRank throughout the web. What’s more, this distribution can be calculated in a straightforward way which does not require iteration as the conventional PageRank algorithm does.

So the PageRank can be calculated much more quickly for relatively small webs and the team has done a simple analysis of the PageRanking of the .eu domain in this way. However, Perra admits that the iterative method would probably be quicker when working with the tens of billions of pages that make up the entire web.

But the great promise of this Schroedinger-like approach is something else entirely. What the wave equation allows is a study of the dynamic behaviour of PageRanking, how the rankings change and under what conditions.

One of the key tools for this is called perturbation theory. It’s no understatement to say that perturbation theory revolutionised our understanding of the universe when it was applied to quantum theory in the 1920s and 1930s.

The promise is that it could do the same to our understanding of the web and if so, this field is in for an interesting few years ahead.

Ref: arxiv.org/abs/0807.4325: Schroedinger-like PageRank equation and localization in the WWW