On computing HITS ExpertRank via lumping the hub matrix

TL;DR

This paper develops a theoretical approach for computing HITS ExpertRank efficiently by lumping dangling nodes in web graphs, revealing insights into the computation of hub and authority vectors.

Contribution

It introduces a lumping method for HITS that handles non-stochastic matrices and clarifies the computation order of hub and authority vectors.

Findings

HITS can be lumped even if the matrix is not stochastic

Hub vectors of nondangling nodes can be computed separately

Authority vectors of nondangling nodes are difficult to compute separately

Abstract

The dangling nodes is the nodes with no out-links in the web graph. It saves many computational cost and operations provided the dangling nodes are lumped into one node. In this paper, motivated by so many dangling nodes in web graph, we develop theoretical results for HITS by the lumping method. We mainly have three findings. First, the HITS model 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, but not vice versa. Third, the authoritative vector of the nondangling nodes is difficult to compute separately from dangling nodes. Therefore, it is better to compute hub vector of the hub matrix in priority, not authoritative vector of the authoritative matrix or them simultaneous.