I had done some similar work sometime back. I have blogged about it here.

I think, that you’re right in saying, that for computations on tags one has to regard these differences between types of tags. For example, the categorical tags of two resources having both “toread” as tag have probably nothing in common.

On the other hand, the use of these “adjectives” differs from user to user, but the one of “categories” from resource to resource, so that it should not bias the global view that much.

I don’t think it’s necessary or even helpful to go to the second level. If tag1-tag2 and tag2-tag3 each are connected strongly and if there is no link between tag1 and tag3 then I’d suggest that tag1 and tag3 don’t belong together. It even could be that tag2 is used differently in context “tag1″ and “tag2″.
Given that tag2=”apple”:
tag1 would be “osx” and tag3=”red”. Then I don’t want to connect osx and red. This example shows that if a tag has got strong connections to two tags which themselves are not connected, this tag is therefore “ambigous” and can have different meanings.
I think the ambigous-algorithm has to go a little bit further..

I suppose that del.icio.us doesn’t go to that “2nd level”. But I didn’t test that out.

say you tagged your article on writing with
“language” and “writing” and a hundred other links connect these two.

similarly there is another mutually exclusive conenction
for “language” and “books”.. now if i build the tag connections the way suggested i cant get a connection between books and writing.
I do agree that in a truly democratic tagging system two tags above “writing” and “books” would eventually get connected.but do u think its necessary to examine more than 1 level of connections? Do you think delicious does it this way?