Exercise Three 1. In one single matlab script le (PageRank408.m), implement: 2. page tranking with damping algorithm; 3. The input three arguments are 1) a link matrix (not normalized) of the pages, 2) a damping factor, and 3) number of iterations ; 4. The output is the importance weight vector of the pages. 5. You could use PageRank test.m for testing your implementation. PageRank test.m is below: names = {'Jimi_1', 'Phillip_2', 'Zhenchao_3', 'Tyler_4', 'Mike_5', 'Stewart_6' ... 'Kurosh_7', 'Jing_8', 'Jeremiah_9', 'Ryan_10', 'Christopher_11', ... 'Yansong_12', 'Neha_13', 'Alexander_14', 'Aidan_15', 'Wesley_16', 'Tristan_17', 'Jacob_18', ... 'Patrick_19', 'Anthony_20', 'Josiah_21', 'Cody_22', 'April_23'}; % % % 1,2,3,4,5,6,7,8,9,1011121314151617181920212223 A = [0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0; %1 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0; %2 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0; %3 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0; %4 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,0; %5 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0; %6 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1; %7 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0; %8 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0; %9 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0; %10 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1; %11 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0; %12 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0; %13 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0; %14 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0; %15 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0; %16 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0; %17 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0; %18 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0; %19 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0; %20 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0; %21 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0; %22 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; %23 %Uncomment the following lines to create a random graph %A = randi([0 1], 23,23); %A(logical(eye(size(A)))) = 0; %run pagerank algorithm with damping factor = 0.85, number of iterations = 1000, pr is the output weight vector of the pages. pr = pagerank(A, 0.85, 1000);

T he iteration expression with damping can be re-written Let R be a matrix with every element equal to 1 RwkWo (The sum of the elements of Wk1 equals 1) Let G dB (1-0)R (G is called the Google matrix) k-1 The iteration formula is equivalent to k-1 so that w is an eigenvector of G