  We present the results of a series of cosmological $N$-body simulations of a
Vector Dark Energy (VDE) model, performed using a suitably modified version of
the publicly available \texttt{GADGET}-2 code. The setups of our simulations
were calibrated pursuing a twofold aim: 1) to analyze the large scale
distribution of massive objects and 2) to determine the properties of halo
structure in this different ramework.We observe that structure formation is
enhanced in VDE, since the mass function at high redshift is boosted up to a
factor of ten with respect to \LCDM, possibly alleviating tensions with the
observations of massive clusters at high redshifts and early reionization
epoch. Significant differences can also be found for the value of the growth
factor, that in VDE shows a completely different behaviour, and in the
distribution of voids, which in this cosmology are on average smaller and less
abundant. We further studied the structure of dark matter haloes more massive
than $5\times10^{13}$\hMsun, finding that no substantial difference emerges
when comparing spin parameter, shape, triaxiality and profiles of structures
evolved under different cosmological pictures. Nevertheless, minor differences
can be found in the concentration-mass relation and the two point correlation
function; both showing different amplitudes and steeper slopes.Using an
additional series of simulations of a \LCDM\ scenario with the same $\Omega_M$
and $\sigma_8$ used in the VDE cosmology, we have been able to establish
whether the modifications induced in the new cosmological picture were due to
the particular nature of the dynamical dark energy or a straightforward
consequence of the cosmological parameters.
