MODELS AND ALGORITHMS FOR PAGERANK SENSITIVITY

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MODELS AND ALGORITHMS FOR PAGERANK SENSITIVITY ( models-and-algorithms-for-pagerank-sensitivity )

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PREFACE For a fun preface to this document, I decided to reflect back on the first PageRank code I ever wrote. Program 1 is a poor implementation of PageRank for all the following reasons: it uses an ugly ; to finish end commands; it uses a terribly inefficient construction to normalize A; it has poor documentation of the parameter e; it doesn’t use compensated summation; it doesn’t include a teleportation parameter; and it doesn’t compute PageRank. These elements constitute a terribly inauspicious start to my work with Page- Rank. I can only hope I’ve learned since writing this first code. Program 1 – An incorrect PageRank implementation. The first PageRank program I wrote, trivially altered to fit on this page. It’s incorrect. See program 2 for a working version. 1 function pgv = pagerank(g, e) 2 % PAGERANK Compute pagerank for graph g. 3 % pgv = pagerank(g) returns the pagerank vector for graph g with default parameters 4 % pgv = pagerank(g, e) returns the pagerank vector for graph g with epsilon = e 5 n = get(g, ’size’); 6 A = g.adj; 7 % normalize A by the degrees of each node 8 degs = degree(g); 9 [i j v] = find(A); 10 for ii = 1:length(i) 11 A(i(ii), j(ii)) = v(ii)./degs(i(ii)); 12 end; 13 init = 1/n*ones(n, 1); 14 pgv = init; 15 delta = Inf; 16 while (delta > e) 17 pgvn = A*pgv; 18 d = norm(pgv, 1) - norm(pgvn, 1); 19 pgvn = pgvn + d*init; 20 delta = norm(pgvn - pgv); 21 pgv = pgvn; 22 end; vii

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