Using the below code, please implement the algorithm for computing PageRank in M

Question

Using the below code, please implement the algorithm for computing PageRank in Matlab. You will need to complete the lines marked with "******".

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function PageRank_incomplete

% This function implements the PageRank algorithm.
dbstop if error; clear; clc; close all;

dDecayFactor = 0.85;

mAdjacencyMatrix = [
0 1 0 0 0; % node 1
0 0 1 1 0; % node 2
0 0 0 1 0; % node 3
1 0 0 0 1; % node 4
0 0 1 0 0; % node 5
];
nNumOfNodes = size(mAdjacencyMatrix,1);

% Node degree matrix
vNodeDegree = sum(mAdjacencyMatrix,2);
mNodeDegreeMatrix = diag(vNodeDegree);
mNodeDegreeMatrixInv = pinv(mNodeDegreeMatrix);

% Compute the node transition probability matrix
mNodeTransProbMatrixP = ; % Please complete this line******

% Compute the PageRank values by using the matrix inverse
mPRMatrix = ; % Please complete this line******
vPRVector1 = sum(mPRMatrix,2) / nNumOfNodes;
disp("Method 1: Matrix Inversion");
disp("PageRank values");
display(vPRVector1);

% Compute the PageRank values by using the iterative method
disp("Method 2: Power Iteration");
vPRVector2 = [];
vTeleportationVector = ones(nNumOfNodes,1) / nNumOfNodes;
vPRVector2_old = vTeleportationVector;
nIdxOfIteration = 0;
while true
    vPRVector2_new = ; % Please complete this line******
    if norm(vPRVector2_new - vPRVector2_old) < 10^(-6)
        vPRVector2 = vPRVector2_new;
        disp("# of iterations");
        disp(nIdxOfIteration);
        break;
    end
    % Please add one line here******
  
    nIdxOfIteration = nIdxOfIteration + 1;
end
disp("PageRank values");
display(vPRVector2);

figure;

Explanation / Answer

PageRank in MATLAB

A MATLAB implementation of the Google PageRank algorithm :

function [ x ] = PageRank( i, j, n, p )

%PAGERANK Calculates the PageRank of the given network.

% param i: Vector of all nodes which are linked to.

% param j: Vector of all nodes which link to other nodes.

% param n: Number of nodes

% param p: Decay rate (optional)

% Note: Node i[k] links to node j[k].

% Reference: https://www.mathworks.com/moler/exm/chapters/pagerank.pdf

if (~exist('p', 'var'))

p = 0.85;

end

G = sparse(i, j, 1, n, n);

c = sum(G, 1);

k = find(c~=0);

D = sparse(k,k,1./c(k),n,n);

e = ones(n, 1);

I = speye(n, n);

x = (I - p*G*D)e;

x = x/sum(x);

end

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