# **SEE-Math**

## Texas A&M University

# **Search and Rank**

## Andrew Raich, David Kerr, David Manuel, Philip Yasskin

When a Search Engine does a search and finds several pages satisfying the search request, how does it rank the results for display on the page (aside from advertising revenue)? It simulates a random walk among the pages and ranks then in the order that the pages were visited (most to least). Students will simulate this by visiting the 5 pages linked below. Then they will compute it by finding the steady state vector of the corresponding probility matrix.

Roll a die and then click on one of the following 5 links. If you roll a 6, roll again.

- Augustin's Page
- Bernhard's Page
- Carl's Page
- David's Page
- Emmy's Page

Continue to roll the die and visit the pages as indicated on each page. Keep track of which pages you visit. The page you visited most often should be ranked highest. The results from all students will be accumulated on the board and compared with the calculated result using probability matrices.

A spreadsheet to accumulate the students page counts is available
here.

A Maple worksheet to compute the probability matrix and it's steady state vector (eigenvector with eigenvalue one) is available
here.

© Philip B. Yasskin, 2013.

Last updated July 1, 2013