LinkRank

There is a new site called LinkRanks, from pubsub.com, that purports to do page-rank-like ranking of domains, based not on regular linking, but on weblog linking:

LinkRanks are our way of measuring the strength, persistence, and vitality of links appearing in weblogs. When PubSub reads a new weblog entry, we pull out any URIs we find and attach them to the entry in a separate field. This allows our users to include domain names or linked file types when creating subscriptions....

Unlike Google's PageRank system, LinkRanks are not iterative. Rather, we base LinkRanks on a simple formula that only looks at local links - links which are within one or two steps of any target site. Also, it's important to note that we only look at links which are in weblog entries - we don't read any of the other links on the page, like the side bars or blogrolls.

Ok. Fair enough. They even go on to describe the formula they use to compute these rankings. Basically, given a source site S and a target site T that it links to, they want to estimate the "relative likelihood" of clicking on the link to T from S. They do this by weighting the importance of the link to T relative to the total number of outbound links from S.

So far so good. But the formula they use is somewhat bizarre. If S0 is the total number of outgoing links from S and S_T is the number of links from S to T (think of T as a domain), then their formula calculates the relative weight of this link as

They then go on to do some standard summing over links etc. What I don't see is: they claim this measures a kind of likelihood that you would click on a link to T from S. But the probability of doing that under a uniform assumption is merely S_T/So. So what model would generate this form ? This is clearly trying to downweight the influence of S_T for small values of So, but how ?

In any case:

If you comment on LinkRanks in your blog, we'd like you to try an experiment with us. In weblog entries that talk about LinkRanks, include this URN somewhere:

http://psi.pubsub.com/20040413:linkranks:1

Consider it done.