The local structure of three hydrogen bonded liquids comprising clusters of markedly different topology: water, methanol, and HF are investigated by analyzing the properties of the Voronoi polyhedra (VP) of the molecules in configurations obtained from Monte Carlo computer simulations. For comparisons, the properties of argon as a nonassociating reference liquid are also calculated. It is found that in liquid HF the fluctuation of the local density is much larger than in the other three liquids, and hence, besides the dense regions, this liquid contains numerous large voids as well. The size of the largest of these voids is found to be commensurate with a cluster of 11 HF molecules, whereas the number of voids as large as one molecule is in the order of the number of molecules. It is found that the number of the hydrogen-bonded neighbors of the HF molecules located at the boundary of such voids does not differ considerably from that of the other molecules, and thus they do not have any specific topological position (e.g., chain terminal) in the hydrogen bonded chains of the molecules. The shape of the VP is found to reflect the arrangement of the nearest neighbors of the molecules. Thus, the VP are considerably less spherical and their topological properties are distributed in a wider range in the associated liquids than in argon. Similarly, in the hydrogen bonded liquids considerably more geometric neighbors are found than the number of molecules belonging to the first coordination shell. On the other hand, in liquid argon, which is a closely packed system, the two values are found to be close to each other. The inhomogeneities of the local density of liquid HF are also reflected in the shape of the VP. The molecules located at the boundary of the large voids are found to have more spherical VP with more and larger faces than the other ones.