LAUSR

The stochastic modification and irreducible modification in PageRank produce large web link changes correspondingly. To get a minimal irreducible web link adjustment, a PageRank model of minimal irreducible adjustment and its lumping method are discussed by Li, Chen, and Song. In this paper, we provide alternative proofs for the minimal irreducible PageRank by a new type of similarity transformation matrices. To further provide theorems and fast algorithms on a reduced matrix, an 4×4 block matrix partition case of the minimal irreducible PageRank model is utilized and analyzed. For some real applications of our results, a lumping algorithm used for speeding up PageRank vector computations is also presented. Numerical results are also reported to show the efficiency of the proposed algorithm.