  Under the commonly used spherical collapse model, we study how dark energy
affects the growth of large scale structures of the Universe in the context of
agegraphic dark energy models. The dynamics of the spherical collapse of dark
matter halos in nonlinear regimes is determined by the properties of the dark
energy model. We show that the main parameters of the spherical collapse model
are directly affected by the evolution of dark energy in the agegraphic dark
energy models. We compute the spherical collapse quantities for different
values of agegraphic model parameter $\alpha$ in two different scenarios:
first, when dark energy does not exhibit fluctuations on cluster scales, and
second, when dark energy inside the overdense region collapses similar to dark
matter. Using the Sheth-Tormen and Reed mass functions, we investigate the
abundance of dark matter halos in the framework of agegraphic dark energy
cosmologies. The model parameter $\alpha$ is a crucial parameter in order to
count the abundance of dark matter halos. Specifically, the present analysis
suggests that the agegraphic dark energy model with bigger (smaller) value of
$\alpha$ predicts less (more) virialized halos with respect to that of
$\Lambda$CDM cosmology. We also show that in agegraphic dark energy models, the
number of halos strongly depends on clustered or uniformed distributions of
dark energy.
