Re: proportionality of hub and authorities and the page-rank

[Subbarao Kambhampati <rao@asu.edu>]

[[To whoever sent this question anonymously--it is best to ask
questions directly, since there is really no way of answering them
other than sending it to mailing list. Even if you are questioning my
answer. Don't worry; my ego is not quite so fragile as to break into
D-sized pieces at the sight of the first question ;-)]

Page rank of a page is proportional to the probability that a random surfer will 
visit this page. This probability is dependent only on the "back
links" and not forward links. So, PR is not related in any direct way
to hub score.

To see this on an example, consider a world containing just 3 pages,
p1, p2 and p3. The only link is from p2 to p3. You can easily see that 
p1 has zero hub and authority; while p2 has hub 1.0; and p3 has
authority 1.0.  *If* hub were to be connected to page rank, than p2
should have a better page rank than p1. Instead, you will notice that
p1 and p2 have basically the same page rank..

Rao
[Mar  7, 2004]





From: CSE494@cotopaxi.eas.asu.edu (WebMonitor mail)
Subject: proportionality of hub and authorities and the page-rank
Date: Thu, 04 Mar 2004 18:17:42 -0700 (MST)
Message-ID: <200403050117.i251HgZ20290@cotopaxi.eas.asu.edu>

CSE494> (message)
CSE494> ---------------------------------------------------------------------------
CSE494> In the solution which you have given, you have just mentioned
CSE494> that the page-rank is more proportional to the
CSE494> authorities. But, there is no justification for this
CSE494> answer. It seems more like an observation than, something with
CSE494> a theoretical or concrete proof behind it. Can you please
CSE494> provide a better explanation of why is it so?
CSE494> 
CSE494> ---->>>>
CSE494> 3.[2pt] Suppose we rank both the PageRank algorithm and the Authorities/Hub algorithm
CSE494> on the same subset of the web-connectivity graph. Is the PageRank value of a page more
CSE494> likely to be proportional to its Hub value or its Authority value? Explain.
CSE494> More likely to be proportional to authorities. In fact, pages that have high hub and low
CSE494> authority values are likely to just have low page ranks.
CSE494> 
CSE494> ---------------------------------------------------------------------------
CSE494>