% Computes website page rank from an adjacency matrix.
%   A   adjacency matrix for web pages
%   q   jump quotient
%
% Returns: google matrix G, page rank vector p
function [G p] = rank(A, q) 
    if nargin < 2; q = 0.15; end

    G = zeros(size(A));
    n = size(A,1);
    s = sum(A,2);

    for r = 1 : n
        for c = 1 : n
            if s(c) > 0
                G(r,c) = q/n + (1 - q)*A(c,r) / s(c);
            else
                G(r,c) = 1/n;
            end
        end
    end

    [V D] = eig(G);

    x = 1;         % Stores index of eigenvalue closest to 1 with i == 0
    for r = 1 : n
        if imag(D(r,r)) == 0 && abs(1 - D(r,r)) < abs(1 - D(x,x))
            x = r;
        end
    end

    p = V(:,x) ./ sum(V(:,x));
end