PageRank.m

function [ rankings ] = PageRank(a, d, epsilon )
%PAGERANK Computes pagerank, returned as a numeric array.
%   A is an adjacent sparse matrix representing a graph
%   d is the dumping factor
%   epsilon defines the threshold to stop 

 g = digraph(a);
 out = outdegree(g);
 n = size(out,1);
 
% Transform adjacency matrix according to WebScience V2, p. 154
% Approaches:
%   * Loop(in-place calculation) needed approx. 200 hours to finish
%   * Built-in PageRank does not return expected result
%   * The following approach could work. 
 a = (spdiags(1./out,0,n,n) * a).';
 
% Get rid off NaN
 a(isnan(a)) = 0;
% Replace zero rows with 1/n.
 a(all(a==0,2),:) = 1/n;

% Initial PageRank 
 rankings = 1 / n * ones(n,1);
 
% Initial error threshold
 delta = Inf;
 while delta > epsilon
  % Save last PR for comparison.
  rankings_prev = rankings;
  rankings = (1 - d) * ones(n,1) + d * a * rankings;
  % Compute error
  delta = norm(rankings-rankings_prev,1);
 end
end