On computing HITS ExpertRank via lumping the hub matrix

The dangling nodes are the nodes with no out-links in the web graph. It saves many computational costs if the dangling nodes are lumped into one node. In this paper, motivated by so many dangling nodes in web graphs, we mainly develop theoretical results for the modified hyperlink-induced topic search (MHITS) model by the lumping method, and the results are also suitable for the HITS model. There are three main findings in the theoretical analysis. First, MHITS can be lumped, although the matrix involved is not stochastic. Second, the hub vector of the nondangling nodes can be computed separately from dangling nodes, and the hub vector of the dangling nodes is parallel to a vector of all ones in MHITS. Third, the authority vector of the nondangling nodes is difficult to compute separately from dangling nodes. The numerical results not only show the feasibility and effectiveness of theoretical analyses, but also demonstrate that the lumped MHITS method can produce a better initial authority vector after the iteration of computing the hub vector.