2021/07/23 by Yongxin Dong, Dong, Yongxin, Yuehua Feng +5
Computer Science · Mathematics · #15A06 #15A18 #15A21 #Advanced Algebra and Logic #Algebraic structures and combinatorial models #FOS: Mathematics #Numerical Analysis (math.NA) #Random Matrices and Applications #cs.NA #math.NA #msc:15A06 #msc:15A18 #msc:15A21
paper · pdf · doi:10.48550/arxiv.2107.11080
14 pages
openalex publication_date 2021/07/23 · arxiv created 2021/11/01 · arxiv updated 2021/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
On the case that the number of dangling nodes is large, PageRank computation can be proceeded with a much smaller matrix through lumping all dangling nodes of a web graph into a single node. Thus, it saves many computational cost and operations. There are also some theoretical contributions on Jordan canonical form of the Google matrix. Motivated by these theoretical contributions, in this note, we provide alternative proofs for some results of Google matrix through the lumping method due to Ipsen and Selee. Specifically we find that the result is also suitable for some subsequent work based on lumping dangling nodes into a node. Besides, an entirely new proof from the matrix decomposition viewpoint is also proposed.