Section A.2 Computer Science: PageRank
Subsection A.2.1 Activities
Activity A.2.1. The $978,000,000,000 Problem.
In the picture below, each circle represents a webpage, and each arrow represents a link from one page to another.
Based on how these pages link to each other, write a list of the 7 webpages in order from most important to least important.
Observation A.2.2. The $978,000,000,000 Idea.
Links are endorsements. That is:
A webpage is important if it is linked to (endorsed) by important pages.
A webpage distributes its importance equally among all the pages it links to (endorses).
Example A.2.3.
Consider this small network with only three pages. Let
splits its endorsement in half between and sends all of its endorsement to sends all of its endorsement to
This corresponds to the page rank system:
Observation A.2.4.
By writing this linear system in terms of matrix multiplication, we obtain the page rank matrix
Thus, computing the importance of pages on a network is equivalent to solving the matrix equation
Activity A.2.5.
Thus, our $978,000,000,000 problem is what kind of problem?
An antiderivative problem
A bijection problem
A cofactoring problem
A determinant problem
An eigenvector problem
Activity A.2.6.
Find a page rank vector
That is, find the eigenspace associated with
Observation A.2.7.
Row-reducing
Therefore, we may conclude that pages
Activity A.2.8.
Compute the
For example, since website
Activity A.2.9.
Find a page rank vector for the given page rank matrix.
Which webpage is most important?
Observation A.2.10.
Since a page rank vector for the network is given by
Based upon this page rank vector, here is a complete ranking of all seven pages from most important to least important:
Activity A.2.11.
Given the following diagram, use a page rank vector to rank the pages
Subsection A.2.2 Slideshow
Slideshow of activities available athttps://teambasedinquirylearning.github.io/linear-algebra/2022/pagerank.slides.html
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