The simple homodinuclear M$ - $M single bonds for group II and XII elements are difficult to obtain as a result of the fulfilled s$ ^2 $ electronic configurations, consequently, a dicationic prototype is often utilized to design the M$ ^+ $$ - $M$ ^+ $ single bond. Existing studies generally use sterically bulky organic ligands L$ ^- $ to synthesize the compounds in the L$ ^- $$ - $M$ ^+ $$ - $M$ ^+ $$ - $L$ ^- $ manner. However, here we report the design of Mg$ - $Mg and Zn$ - $Zn single bonds in two ligandless clusters, Mg$ _2 $B$ _7 $$ ^- $ and Zn$ _2 $B$ _7 $$ ^- $, using density functional theory methods. The global minima of both of the clusters are in the form of M$ _2 $$ ^{2+} $(B$ _7 $$ ^{3-} $), where the M$ - $M single bonds are positioned above a quasi-planar hexagonal B$ _7 $ moiety. Chemical bonding analyses further confirm the existence of Mg$ - $Mg and Zn$ - $Zn single bonds in these clusters, which are driven by the unusually stable B$ _7 $$ ^{3-} $ moiety that is both $ \sigma $ and $ \pi $ aromatic. Vertical detachment energies of Mg$ _2 $B$ _7 $$ ^- $ and Zn$ _2 $B$ _7 $$ ^- $ are calculated to be 2.79 eV and 2.94 eV, respectively, for the future comparisons with experimental data.