A Survey of Google’s PageRank
Calculation of Page Rank, Page Rank Implementation, Inbound Links, Outbound Links, Number of Pages, PageRank Distribution, Additional Factors and more.
The Lineal Algebra Behind Google
The $25,000,000,000 Eigenvector - The Linear Algebra Behind Google. Google’s success derives in large part from its PageRank algorithm, which ranks the importance of webpages according to an eigenvector of a weighted link matrix. Analysis of the PageRank formula provides a wonderful applied topic for a linear algebra course.
The Intelligent Surfer: Probabilistic Combination of Link and Content Information in PageRank

We propose to improve Page-Rank by using a more intelligent surfer, one that is guided by a probabilistic model of the relevance of a page to a query. Efficient execution of our algorithm at query time is made possible by precomputing at crawl time (and thus once for all queries) the necessary terms.

Topic-Sensitive PageRank
To yield more accurate search results, we propose computing a set of PageRank vectors, biased using a set of representative topics, to capture more accurately the notion of importance with respect to a particular topic. By using these (precomputed) biased PageRank vectors to generate query-specific importance scores for pages at query time, we show that we can generate more accurate rankings than with a single, generic PageRank vector.

Method for node ranking in a linked database
A method assigns importance ranks to nodes in a linked database, such as any database of documents containing citations, the world wide web or any other hypermedia database. The rank assigned to a document is calculated from the ranks of documents citing it. In addition, the rank of a document is calculated from a constant representing the probability that a browser through the database will randomly jump to the document. By Page and Lawrence.

How Google Finds Your Needle in the Web’s Haystack
Mathematical Background of Google PageRank. By David Austin, Grand Valley State University
A Large-Scale Hypertextual Web Search Engine
Original Slides, by Larry Page.
Wikipedia: PageRank
Mathematical Theory Behind Google PageRank