The accurate description of the vector hollow Gaussian beam (HGB) in the far-field is a sum of two orthogonal terms: the TE and TM terms. The TE term denotes the electric field transverse to the propagation axis, and the TM term the associated magnetic field transverse to the propagation axis. The structural properties of a vector HGB, which are related to the energy flux distributions of the HGB and its TE and TM terms, are investigated in the far-field. The analytical expressions for the ratios of the powers of the TE and TM terms to that of the HGB are presented without any approximation. The contributions of the powers of the TE and TM terms to the power of the HGB are determined by the f-parameter and the beam order. The analytical formulae of the far-field divergence angles of the TE term, the TM term, and the HGB, which are defined by the second-order moment of the energy flux, are derived. The divergence angles depend on the f-parameter and the beam order. A relation among the divergence angles of the TE term, the TM term, and the HGB are also presented. The influences of the f-parameter and the beam order on the structural properties of a vector HGB are numerically examined in the far-field.