By density functional theory method (B3LYP, basis 6-31G**) the equilibrium spatial structure and the electronic structure have been calculated of carbon nanoclusters (CNC) derived from the nanocluster C96 of hexagonal shape due to removing one or two atoms. For comparison, the calculations have been carried out of similar structures formed from polycyclic aromatic molecules (PAM) C96H24 due to removal on one or two carbon atoms also. It has been show that: the ground electronic states of CNC C96-1(1), C96-2(1), and C96-1(1)H24 systems are triplet, while that of the system C96-2(1)Н24 - quintet; the creation of a monovacancy in the central hexagon of CNC C96 does not violate the isolation of the conjugated system of the peripheral chain of carbon atoms, as in the case of defect-free CNC C96 hexagonal structure; spectrum of single-electron energy levels of the clusters containing vacancies includes the energies of several frontier vacant MOs localized at the cyclic peripheral chain belonging into the range of energies of the highest occupied MO; the removal of one atom from the central hexagon CNC C96 results in a "friable" structure of the formed cluster C96-1(1), what is reflected in the reduction of the removal energy for the second carbon atom from the C96-1(1); removing carbon atom of PAM C96H24 stabilizes the resulting system what is evidenced by the growth of the formation energy of the second monovacancy compared to that of the first one; the properties of CNC containing vacancies differ from those of the systems obtained from PAM due to removal of carbon atoms.