The simple homodinuclear M-M single bonds for Group II and XII elements are difficult to obtain as a result of the fulfilled s2 electronic configurations, consequently, a dicationic prototype is often utilized to design the M+-M+ single bond. Existing studies generally use sterically bulky organic ligands L- to synthesize the compounds in an L--M+-M+-L- manner. However, here we report the design of Mg-Mg and Zn-Zn single bonds in two ligandless clusters, Mg2B7- and Zn2B7-, using density functional theory methods. The global minima of both of the clusters are in the form of M22+(B73-), where the M-M single bonds are positioned above a quasi-planar hexagonal B7 moiety. Chemical bonding analyses further confirm the existence of Mg-Mg and Zn-Zn single bonds in these clusters, which are driven by the unusually stable B73- moiety that is both σ and π aromatic. Vertical detachment energies of Mg2B7- and Zn2B7- are calculated to be 2.79 eV and 2.94 eV, respectively, for the future comparisons with experimental data.