Bond lengths and bond indices in As20, Ni12As20, [As@Ni12As20]3–, As@C60, and As@C70 clusters were calculated by the DFT PBE0/SDD method. The oxidation and reduction degrees of the endo-atom and the shell are expressed in terms of the populations of one-electron states localized in these components of the complexes. Each arsenic atom in clusters has an entirely localized lone electron pair. The arsenic atom inside fullerenes retains the electronic configuration and spin of the free arsenic atom ground state. Inside the [Ni12As20]6– shell, it has the oxidation state 3+. There is no covalent bond between the endo-atom and the shell in the clusters. The bond indices refute the opinion about the “onion” [As@Ni12@As20]3– structure: the nickel atoms are not bonded to each other and the As–As bond indices are three times lower than in As20.