MN - Google PageRank Algorithm

->This program was implemented in Octave => Install octave

->The first task implements the Iterative version of the algorithm

• I make the system matrix in a separate matrix in which if there is a link from i to j then we have a link and put 1 in M ​​[i] [j].

• At the same time I find out the link vector.

• I find the link matrix M and calculate it according to the formula.

• Iterations stop when the difference between two Pagerank vectors consecutive is less than the given error

->The second requirement involves the algebraic implementation of the algorithm

• Same story as above, but you will need to calculate rank knowing that :

   R = (d*M + ( 1 - D)/ nr*E)*R cu E*R= 1, so

   R = (I - d*M)^(-1) * ( 1 - d ) / nr

• The last relation represents a superior triangular system, which is solved by the SST() method.

For the third requirement

• I put all the data in the file. :)

• We sorted the descending vector and looked for the initial position of each element in the sorted vector in the initial one

• To find the affiliation we applied the function of U(X) and we found the values ​​of the variables a and b according to the known val_1 and val_2.

• To find the two varaible a si b make a sistem at limit val1 and val2:

  1 = a*val2 + b

  0 = a*val1 + b

  ---------------> substract

  1 = a*(val2 - val1)

  b = a - a * val1

Documentation:

• https://en.wikipedia.org/wiki/PageRank
• https://www.gnu.org/software/octave

->Feedback

A very interesting topic that made me quite curious about what happens behind a search engine that I use every day.