Problem 2. (45 points) A network of webpages is shown as follows: (a) Write out the H matrix of the network. ( 9 points.) (b) Is (are) there any dangling node(s)? If yes, who is that (are they)? (4 points.) Write out the H^ matrix that has the dangling node(s), if any, fixed. (4 points.) 1 (c) Although there is no island in the network, please still add randomization to get: G=H^+(1)N111T, where =0.95, and N is the total number of webpages. (4 points.) (d) Initialize the importance scores of the webpages as: T[0]=[N1,N1,,N1]. Run PageRank algorithm T[t]=T[t1]G for t=1,2,3,,T, where T=15. Plot the records of 2[t],4[t],6[t] for t=0,1,2,3,T. (15 points; clearly mark and differentiate the three plots or draw them separately.) At [T], which webpage has the highest importance score? ( 2 points.) Which has the lowest? ( 2 points.) (e) Use eigen-decomposition of GT to find the vector of importance scores , and compare it with [T] obtained above. (5 points.) Note: For (c)(d)(e), you may want to write a program (in any language; feel free to reuse and adapt the sample codes on Blackboard). Please paste your plots and source codes in the same PDF submission of your