  Using ab initio methods based on density functional theory, the electronic
and magnetic structure of layered hexagonal NbSe$_{2}$ is studied. In the case
of single-layer NbSe$_{2}$ it is found that, for all the functionals
considered, the magnetic solution is lower in energy than the non-magnetic
solution. The magnetic ground-state is ferrimagnetic with a magnetic moment of
1.09 $\mu_{B}$ at the Nb atoms and a magnetic moment of 0.05 $\mu_{B}$, in the
opposite direction, at the Se atoms. Our calculations show that single-layer
NbSe$_{2}$ does not display a charge density wave instability unless a graphene
layer is considered as a substrate. Then, two kinds of 3$\times$3 charge
density waves are found, which are observed in our STM experiments. This
suggest that the driving force of charge instabilities in NbSe$_{2}$ differ in
bulk and in the single-layer limit. Our work sets magnetism into play in this
highly-correlated 2D material, which is crucial to understand the formation
mechanisms of 2D superconductivity and charge density wave order.
