We provide flux-and volume-limited galaxy group and cluster catalogues based on the spectroscopic sample of the galaxies of SDSS data release 10. We used a modified friends-of-friends method with a variable linking length in the transverse and radial directions to identify as many realistic groups as possible. The flux-limited catalogue incorporates galaxies down to m r = 17.77 mag. It includes 588 193 galaxies and 82 458 groups. The volume-limited catalogues are complete for absolute magnitudes down to M r,lim = −18.0, −18.5, −19.0, −19.5, −20.0, −20.5, and −21.0; the completeness is achieved within different spatial volumes. Our analysis shows that flux-and volume-limited group samples are well compatible, especially for the larger groups/clusters. Dynamical mass estimates based on radial velocity dispersions and group extent in the sky were added to the extracted groups.

The main feature of the spatial large-scale galaxy distribution is its intricate network of galaxy filaments. This network is spanned by the galaxy locations that can be interpreted as a three-dimensional point distribution. The global properties of the point process can be measured by different statistical methods, which, however, do not describe directly the structure elements. The morphology of the large scale structure, on the other hand, is an important property of the galaxy distribution. Here we apply an object point process with interactions (the Bisous model) to trace and extract the filamentary network in the presently largest galaxy redshift survey, the Sloan Digital Sky Survey (SDSS). We search for filaments in the galaxy distribution that have a radius of about 0.5 h −1 Mpc. We divide the detected network into single filaments and present a public catalogue of filaments. We study the filament length distribution and show that the longest filaments reach the length of 60 h −1 Mpc. The filaments contain 35-40% of the total galaxy luminosity and they cover roughly 5-8% of the total volume, in good agreement with N -body simulations and previous observational results.

We have constructed a set of supercluster catalogues for the galaxies from the SDSS survey main and luminous red galaxy (LRG) flux-limited samples. To delineate superclusters, we calculated luminosity density fields using the B 3 -spline kernel of the radius of 8 h −1 Mpc for the main sample and 16 h −1 Mpc for the LRG sample and define regions with densities over a selected threshold as superclusters, while utilising almost the whole volume of both samples. We created two types of catalogues, one with an adaptive local threshold and a set of catalogues with different global thresholds. We describe the supercluster catalogues and their general properties. Using smoothed bootstrap, we find uncertainty estimates for the density field and use these to attribute confidence levels to the catalogue objects. We have also created a test catalogue for the galaxies from the Millennium simulation to compare the simulated and observed superclusters and to clarify the methods we use. We find that the superclusters are well-defined systems, and the properties of the superclusters of the main and LRG samples are similar. We also show that with adaptive local thresholds we get a sample of superclusters, the properties of which do not depend on their distance from the observer. The Millennium galaxy catalogue superclusters are similar to those observed.