  We study large-scale structures from numerical simulations, paying particular
attention to supercluster-like structures. A grid-density-contour based
algorithm is adopted to locate connected groups. With the increase of the
linking density threshold, the foam- like cosmic web is subsequently broken
into individual supercluster-like groups and further halos which are in
accordance to groups with the linking density threshold {\rho}/{\rho}= 1 +
{\delta} = 80. By analyzing sets of cosmological simulations with varying
cosmological parameters, we find that an universal mass function exists not
only for halos but also for low-density supercluster-like groups until the
linking density threshold decreases to a density where the global percolation
of large-scale structures occurs. We further show that the mass functions of
different groups can be well described by the Jenkins form with the parameters
being dependent on the linking density threshold. On the other hand, these low-
density supercluster-like groups cannot be directly associated with the
predictions from the excursion set theory with effective barriers obtained from
dynamical collapse models, and the peak exclusion effect must be taken into
account. Including such an effect, the mass function of groups with the linking
density threshold 1 + {\delta} = 16 is in good agreements with that from the
excursion set theory with a nearly flat effective barrier. A simplified
analysis of the ellipsoidal collapse model indicates that the barrier for
collapses along two axes to form filaments is approximately flat in scales,
thus we define groups identified with 1 + {\delta} = 16 as filaments. We then
further study the halo-filament conditional mass function and the filament-halo
conditional mass function, and compare them with the predictions from the
two-barrier excursion set theory. The shape statistics for filaments are also
presented.
