Google Page Rank

If we have: P will be:

Problem

• We do not have a unique unique steady-state for all pages
• pages that do not link to other pages can have the largest importance, or highest PageRank

Fix

• If a user reaches a page that does not link to other pages, the user will choose any page in the web, with equal probability, and move to that page.
• Corresponding fixed matrix:

WHY

This works because we are taking each column and reducing its sum by $(1-p)$. Then we are adding $(1-p)$ back to the column, but evenly distributed over the whole column. This insures that the sum of the column of the final matrix stays $=1$.