In this paper, a homotopy continuation method for the computation of nonnegative
Z-/H-eigenpairs of a nonnegative tensor is presented. We show that the homotopy
continuation method is guaranteed to compute a nonnegative eigenpair.
Additionally, using degree analysis, we show that the number of positive
Z-eigenpairs of an irreducible nonnegative tensor is odd. A novel homotopy
continuation method is proposed to compute an odd number of positive Z-eigenpairs, and some numerical results are presented.