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:
                                                                                                                                                                \(R\left(u\right)=c\sum_{v\in B_u}^{ }\frac{R\left(v\right)}{N_v}\)