Morphological Statistics of the Cosmic Web

We report the {\em first} systematic study of the supercluster-void network in the $\Lambda$CDM concordance cosmology treating voids and superclusters on an equal footing. We study the dark matter density field in real space smoothed with the $L_s = 5$ \hm1 Mpc Gaussian window. Superclusters and voids are defined as individual members of over-dense and under-dense excursion sets respectively. We determine the morphological properties of the cosmic web at a large number of dark matter density levels by computing Minkowski functionals for every supercluster and void. At the adopted smoothing scale individual superclusters totally occupy no more than about 5% of the total volume and contain no more than 20% of mass if the largest supercluster is excluded. Likewise, individual voids totally occupy no more than 14% of volume and contain no more than 4% of mass if the largest void is excluded. The genus of individual superclusters can be $\sim 5$ while the genus of individual voids reaches $\sim 55$, implying significant amount of substructure in superclusters and especially in voids. Large voids are typically distinctly non-spherical.