Write another function whose input is the page rank vector and a vector of strings called url that specifies the corresponding URLs. Use the built-in function sort to sort the page rank vector and print the corresponding URLs in order from highest to lowest page rank. The second output of sort returns an index vector that can be used to order the URLs.
Run your program on the adjacency matrices M and URLs url defined in the following Matlab data files (access the data with "load filename"):
As we discussed in class, the rate of convergence depends on the second largest of the absolute values of the eigenvalues of the Google matrix: the closer this is to 1, the slower the convergence. Modifying the power method to compute this eigenvalue is a little beyond the scope of this class, so instead, compute the Google matrix G explicitly for the nyu20.mat data (in contrast to the previous question, where it is important not to compute G explicitly), and compute all the eigenvalues by calling the built-in function eig. Then look at the eigenvalue absolute values using abs (the absolute value of a complex number is the square root of the sum of the squares of the real and imaginary parts). Investigate the truth of the claim in the 4th paragraph of p.11 of the Austin paper: that the second largest of the absolute values of the eigenvalues is alpha. If this claim is true, print output to support it. If it's not, figure out what Austin intended to say instead, printing output to support your claim.
Submit the homework, including function listings and everything else requested above, either by hard copy left under my office door or as a single pdf file which should be emailed directly to me.