We introduce a partition of the web pages particularly suited to the PageRank problems in which the web link graph has a nested block structure. Based on the partition of the web pages, dangling nodes, common nodes, and general nodes, the hyperlink matrix can be reordered to be a more simple block structure. Then based on the parallel computation method, we propose an algorithm for the PageRank problems. In this algorithm, the dimension of the linear system becomes smaller, and the vector for general nodes in each block can be calculated separately in every iteration. Numerical experiments show that this approach speeds up the computation of PageRank.
Yue Xie. Ting-Zhu Huang. Chun Wen. De-An Wu. "An Improved Approach to the PageRank Problems." J. Appl. Math. 2013 1 - 8, 2013. https://doi.org/10.1155/2013/438987