We started to read Chapter 9 of "Mathematics and Techonology" by Ch. Rousseau and Y. Saint-Aubin .
The main idea of the PageRank algorithm is not to judge a website by its content, but rather by how often a randomly clicking websurfer will return to it. If we represent a collection of websites by a directed graph (edges of the graph represent links from one website to another), then we have to discuss random walks on graphs. We discussed Markov property of the random walk, and defined transition matrix P. We finished by noticing that a limiting probability vector p, if exists, should satisfy p=Pp, i.e. to be an eigenvector with eigenvalue equal to 1.
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