  \emph{Ab initio} calculations of the structure and electronic density of
states (DOS) of the perfect core-shell $Ag_{27}Cu_{7}$ nanoalloy attest to its
$D_{5h}$ symmetry and confirm that it has only 6 non-equivalent (2 $Cu$ and 4
$Ag$) atoms. Analysis of bond-length, average formation energy, heat of
formation of $Ag_{27}Cu_{7}$ and $L1_2$ $Ag-Cu$ alloys provide an explanation
for the relative stability of the former with respect to the other nanoalloys
in the same family. The HOMO-LUMO gap is found to be 0.77 eV, in agreement with
previous results. Analysis of the DOS of $Ag_{27}Cu_{7}$, $L1_2$ $Ag-Cu$ alloys
and related systems provides insight into the effects of low coordination,
contraction/expansion and the presence of foreign atoms on the DOS of $Cu$ and
$Ag$. While some characteristics of the DOS are reminiscent of those of the
phonon-stable $L1_2$ $Ag-Cu$ alloys, the $Cu$ and $Ag$ states hybridize
significantly in $Ag_{27}Cu_{7}$, compensating the $d$-band narrowing that each
atom undergoes and hindering the dip in the DOS found in the bulk alloys.
Charge density plots of $Ag_{27}Cu_{7}$ provide further insights into the
relative strengths of the various interatomic bonds. Our results for the
electronic and geometric structure of this nanoalloy can be explained in terms
of length and strength hierarchies of the bonds, which may have implications
also for the stability of alloy in any phase or size.
