This paper gives an example of some of the flaws with Google's PageRank algorithm and they suggest they have an algorithm that fixes it. Something is Wrong with Google’s Mathematical Model "In their original paper : ”The PageRank Citation Ranking: Bringing Order to the Web” , Page et al. suggest a new ranking algorithm named - PageRank. It is shown there that implementing the new algorithm boils down to solving a huge eigenvalues problem Ax = x (1) where A is a matrix which represents a graph related to the web. It is claimed that in order for the model to work properly, the graph should be strongly connected. In general, the graph is not strongly connected and we have ’sink’ set of pages."
"We have developed a new algorithm which can be considered as a modification of the original PageRank algorithm. The modified algorithm is stable and gives a correct ranking vector. The mathematical complexity of the suggested algorithm is the same as the complexity of the original one."
In Google's Librarian Center they've published as similar explanation of PageRank called "How does Google collect and rank results?".