  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.
