Consider the link graph 4 First, construct the L, the link matrix, as discussed in Section 5.5 on the HITS algorithm. Then do the following: 1. Start by assuming the hubbiness of each node is 1; that is, the vector h is (the transpose of) (1,1,1,1). 2. Compute an estimate of the authority vector a=LTh. 3. Normalize a by dividing all values so the largest value is 1. 4. Compute an estimate of the hubbiness vector h=La. 5. Normalize h by dividing all values so the largest value is 1. What would be the estimate on a = [a1, a2, a3, a4] after the first round of iteration? Use simplified fractions to answer. a1 = a 2 = a3 = a4 = What would be the estimate on h = [h1, h2, h3, h4] after the first round of iteration? Use fractions to answer. h1 = h2 = h3 = h4 = Consider three Web pages with the following links: A B C Suppose we compute PageRank with teleport and set to 0.7, and we introduce the additional constraint that the sum of the PageRanks of the three pages must be 3, i.e. each node has an initial PageRank of 1 (This is different from the book which sets the initial PageRank to 1. However, this doesn't matter, because any multiple of a solution will also be a solution.) Compute the final PageRanks a, b, and c of the three pages A, B, and C, respectively (Please use decimal number to fill in the blanks) PageRank a = PageRank b = PageRank c =