  In this paper we define a set of numerical criteria for a handlebody link to
be irreducible. It provides an effective, easy-to-implement method to determine
the irreducibility of handlebody links; particularly, it recognizes the
irreducibility of all handlebody knots in the Ishii-Kishimoto-Moriuchi-Suzuki
knot table and most handlebody links in the Bellettini-Paolini-Paolini-Wang
link table.
