# what is r. in the pagerank algorithm

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Kellie on 10 Apr 2023
Commented: Askic V on 11 Apr 2023
I was reading Matlabs Pagerank algorithm and I was hoping that someone can clarify what the r. is within the equation. I have all the other elements just not sure what r.
Thank you!

Askic V on 10 Apr 2023
Hi Kellie,
you probably mean on the following equation:
r = (1-P)/n + P*(A'*(r./d) + s/n);
% r is a vector of PageRank scores.
% P is a scalar damping factor (usually 0.85), which is the probability that a random surfer clicks on a link on the current page, instead of continuing on another random page.
% A' is the transpose of the adjacency matrix of the graph.
% d is a vector containing the out-degree of each node in the graph. d is set to 1 for nodes with no outgoing edges.
% n is the scalar number of nodes in the graph.
% s is the scalar sum of the PageRank scores for pages with no links.
So, this equation updates the vector of Pagerank scores based on the current value of vector r and other parameters.
Specifically,
r./d
is an element-wise division, which means that each element of r is divided with its corresponding element in vector d (the vector d contains same number of elements like vector r).
Kellie on 11 Apr 2023
Thank you Askic that has helped so much! one more question, if you are assessing a matrix (A) is it G = digraph(A,[],names);?
Thank you! :)
Askic V on 11 Apr 2023
Matrix A is an adjacency matrix of a graph G.
If you want to create a directed graph based on the adjacency matrix, then you simply use the following syntax:
G2 = digraph(A)
In the example code above, matrix A is simply:
A =
0 1 0 0 1 0
0 0 1 1 0 0
0 0 0 1 1 1
1 0 0 0 0 0
1 0 0 0 0 0
0 0 0 0 0 0
If A(i,j) is 1 that means there is a directed connection from i to j.

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