Web pages vary greatly in terms of the number of backlinks they have. For example, the
Netscape home page has 62,804 backlinks in our current database compared to most pages which
have just a few backlinks. Generally, highly linked pages are more "important" than pages with
few links. Simple citation counting has been used to speculate on the future winners of the Nobel
Prize \cite{Sankaran.}. PageRank provides a more sophisticated method for doing citation counting.
The reason that PageRank is interesting is that there are many cases where simple citation
counting does not correspond to our common sense notion of importance. For example, if a web
page has a link o the Yahoo home page, it may be just one link but it is a very important one.
This page should be ranked higher than many pages with more links but from obscure places.
PageRank is an attempt to see how good an approximation to "importance" can be obtained just
from the link structure.
2.3 Propagation of Ranking Through Links
Based on the discussion above, we give the following intuitive description of PageRank: a page has
high rank if the sum of the ranks of its backlinks is high. This covers both the case when a page
has many backlinks and when a page has a few highly ranked backlinks
2.4 Definition of PageRank
Let \(u\) be a web page. Then let \(F_u\) be the set of pages \(u\) points to and \(B_u\) be the set of pages that
point to \(u\). Let \(N_u=\left|F_u\right|\) be the number of links from \(u\) and let \(c\) be a factor used for normalization
(so that the total rank of all web pages is constant).
We begin by defining a simple ranking, R which is a slightly simplified version of PageRank:
\(R\left(u\right)=c\sum_{v\in B_u}^{ }\frac{R\left(v\right)}{N_v}\)