Globally said, to become famous on the internet, i.e. get a high rank in a search engine, you need many high ranking websites (not dummy ones you make yourself ) referring to your site. The ranking is relative with respect to the structure of the web. To find the ranking requires solving some numerical equality to obtain a fixed point in a procedure. The basis is a square matrix Q with entrances Q_ij? 0 if there is no link from web j to i and a value N_j if there is, where N_j is the total number of outgoing links in web j. Notice that the sum of the columns of Q is 1 and the number of nonzeros in a row gives the number of sites that link to i. If the ranking is given by a vector r, we "simply" have to solve r=Qr. Given that r should sum to one, be nonnegative and Q has billions of rows, it does not feel easy to find a ranking. There is the possibility to use the power method. This method multiplies the iterative vector r_k with the matrix and normilizes it such that the sum is one. The convergence depends in fact on the second eigenvalue. The smaller that is, the faster the convergence.

Eligius Hendrix

University of Malaga