GOOGLE MATRIX

The Google Matrix is a mathematical matrix used in Google’s PageRank algorithm to rank web pages based on the structure of links between them.

What is the Google Matrix?

The Google Matrix is a square matrix that represents the probability of moving from one webpage to another by following hyperlinks.

It is commonly written as:$$G = \alpha S + (1-\alpha)\frac{1}{N}E$$G=αS+(1−α)N1​E

where:

• GGG = Google Matrix
• α\alphaα = damping factor (usually 0.85)
• SSS = normalized link matrix (shows how pages link to each other)
• NNN = total number of web pages
• EEE = matrix with all entries equal to 1

Why is it used?

The Google Matrix helps determine the importance of web pages by modeling the behavior of a “random surfer”:

• With probability 0.85, the surfer follows a hyperlink.
• With probability 0.15, the surfer jumps to any random page.

The steady-state probabilities of this process become the PageRank scores