The problem is essentially this: since pagerank is basically the probability that a random walk through the link graph will end up on your site, linking back to yourself, and no other websites, gives a big boost to your pagerank because a random walk will get stuck on your site. Of course it’s easy to just ignore self-links, but you can get essentially the same effect through clique-like groups of websites and this can be more difficult to detect.
What’s interesting is that an algorithm based on how electrical current flows (so a link is a one-way resistor, i.e. a resistor in series with a diode) would not have this problem. Attaching a conductive loop to some point in a circuit does not change how current flows. Electrons don’t get stuck in loops because they don’t drift around randomly, they move from lower voltage to higher voltage.
Link graphs remind me of lightning descending leaders. If you can have a sense of charge potential between cloud and ground, there might be a circuit equivalent which drains largely self-referential link-farms.
Or is that rephrasing your description? My circuit physics / EE-fu is exceedingly weak.
I think so? There is an obvious circuit equivalent where links are interpreted as one-way resistors. You get a charge potential automatically given the circuit and a choice of source / sink nodes (which you need to decide on anyway to apply pagerank).
Cluster analysis generally shows such relations though.
(I'm pretty sure these questions have generated multiple PhDs at Google.)
I have a feeling that you think the electrical potential must be defined by some ad-hoc method before applying an electrical algorithm, and this requires fancy techniques like cluster analysis and the like? This is not the case. Let me re-emphasize that you only need to specify the network of resistors (which is the link graph) and the source and sink, and then the potential is defined automatically in terms of those things (the same way as in physical circuits).
The source and sink are arbitrary? Or do they need to correspond to some actual reality?
In regards to the question, the latter. The source corresponds roughly to the E vector of the pagerank whitepaper. It's a set of websites that's axiomatically good. The pagerank paper suggested the Netscape home page and John McCarthy's homepage as examples, or alternatively making every website a source, although the last option is more prone to abuse. The sink is harder to find a good analogy for. I think a reasonable choice would be to add a new node to the graph representing the sink, and then connect every website via a directed resistor. Then websites could be ranked by how much current flows through the resistor to the sink.
Edit: By the way, upon thinking about this more, I've just realized that I'm not sure about the exact mechanism by which link farms boost pagerank. As far as I can tell there are two possibilities:
A. The original "stuck in a loop" explanation, by which you can illegitimately magnify legitimately earned rank.
B. With the every-page-as-source strategy, you can boost the rank of a website by creating a new website and linking to it, even if nothing links to the new website. Then the other extra links in the link farm just exist to avoid detection of this sort of thing. So you are illegitimately creating rank from scratch, rather than magnifying existing rank.
Admittedly the electrical circuit thing only addresses mechanism A. Mechanism B can be addressed by being more discriminating about which websites are in the source. That applies whether you use pagerank or the electrical thing.
And I'll claim my prize to the second ;-)
The signal will be hugely susceptible to outlier bias -- The Post That Goes Viral, and generates a huge number of incoming links -- will dominate the rankings.
Because the signal is so thin, distorting and manipulation (through link farming) will be cheap and difficult to detect (a small number of links across a large number of sites).
Don't get me wrong: looking at incidental behaviour is useful, and can often be much more beneficial than direct actions. But remember that all of these signals are actually proxies for some ineffible quantity you're trying to measure, quality.
(The very definition of which should leave you crying on the floor after a few hours. Or days. Or weeks. Or months. Or years....)
May minds have attempted this task. All have fail.
Your correspondent included.
(Small site, many moons ago, since surrendered its electrons back to the Great Disk in the Sky.)