  Using spin polarized density functional theory (DFT) based calculations,
combined with ab-initio molecular dynamics simulation, we carry out a
systematic investigation of the bimetallic Ni$_{13-n}$Ag$_n$ nano clusters, for
all compositions. This includes prediction of the geometry, mixing behavior,
and electronic properties. Our study reveals a tendency towards formation of a
core-shell like structures, following the rule of putting Ni in high
coordination site and Ag in low coordination site. Our calculations predict
negative mixing energies for the entire composition range, indicating mixing to
be favored for the bimetallic small sized Ni-Ag clusters, irrespective of the
compositions. The magic composition with the highest stability is found for the
NiAg$_{12}$ alloy cluster. We investigate the microscopic origin of core-shell
like structure with negative mixing energy, in which the Ni-Ag inter-facial
interaction is found to play role. We also study the magnetic properties of the
Ni-Ag alloy clusters. The Ni dominated magnetism, consists of parallel
alignment of Ni moments while the tiny moments on Ag align in anti-parallel to
Ni moments. The hybridization with Ag environment causes reduction of Ni
moment.
