Another try on answering Zheshen's qn on why have Authorities defined in terms of Hubs and vice versa..

Implicit in my discussion of kings and king-makers is the point that "kings" normally don't point to others (they are kings); Kingmakers do.. (if you want
a more operatic and gender-neutral metaphor, primadonnas don't necessarily point to other primadonnas. Impresarios point to primadonnas.)

In other words, pages with high authority don't *necessarily* point to other pages with high authority. This is why we find it better to define authorities
in terms of hubs and vice versa

(Note that if an authority u happens to be too gracious for its own good
and  does deign to point to another authority v, the A/H model will still catch it-- u will have both a high authority and high hub value..

This is not surprising. In science you value a single paper both for its "originality" (authority) and its "graciousness" in citing all relevant prior work
(hub). Just because you are not gracious doesn't mean you are not an authority--you are just an ungracious authority.

Anecdote:
As you probably know, for the longest time  Newton held a grudge against Leibnitz who, for all practical purposes, had invented calculus independently and
had even gave it a much more natural notation--the one we use today. Newton did invent calculus (what he called the theory of "fluxions" ) much earlier--but never
bothered to publicize it (or even start a company..). He hated Leibnitz's claim to calculus so much that he ran a highly organized scientific vendetta against Leibnitz
both while he was living and after his death.. (in one particularly flagrant incident, Newton, as the president of Royal Society, started an "impartial" --wink wink--scientific committee
to investigate who deserves the credit for calculus--he or leibnitz, staffed the committee with his friends, and not wanting to take a chance, even *wrote* the
committee's final report!).  Newton is thus a classic case of ungracious authority... (he also had a long standing rivalry with Hooke--the guy who analyzed elasticity).


A sweet contrast is Gauss, who too discovered and opened more areas of Math than he ever had the time to publish. The story goes that when Jacobi went to him
to show him his great discoveries in group theory, Gauss went to the back of his room, opened some dusty folders and showed him 20-year old manuscripts written by him (Gauss) which basically did all the work. He however, didn't begrudge Jacobi his fame...

---end anecdote--

Rao