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.

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Aims. We study the morphology of a set of superclusters drawn from the SDSS DR7. Methods. We calculate the luminosity density field to determine superclusters from a flux-limited sample of galaxies from SDSS DR7 and select superclusters with 300 and more galaxies for our study. We characterise the morphology of superclusters using the fourth Minkowski functional V 3 , the morphological signature (the curve in the shapefinder's K 1 -K 2 plane) and the shape parameter (the ratio of the shapefinders K 1 /K 2 ). We investigate the supercluster sample using multidimensional normal mixture modelling. We use Abell clusters to identify our superclusters with known superclusters and to study the large-scale distribution of superclusters. Results. The superclusters in our sample form three chains of superclusters; one of them is the Sloan Great Wall. Most superclusters have filament-like overall shapes. Superclusters can be divided into two sets; more elongated superclusters are more luminous, richer, have larger diameters and a more complex fine structure than less elongated superclusters. The fine structure of superclusters can be divided into four main morphological types: spiders, multispiders, filaments, and multibranching filaments. We present the 2D and 3D distribution of galaxies and rich groups, the fourth Minkowski functional, and the morphological signature for all superclusters. Conclusions. Widely different morphologies of superclusters show that their evolution has been dissimilar. A study of a larger sample of superclusters from observations and simulations is needed to understand the morphological variety of superclusters and the possible connection between the morphology of superclusters and their large-scale environment.

Abstract. We propose to apply a marked point process to automatically delineate filaments of the large-scale structure in redshift catalogues. We illustrate the feasibility of the idea on an example of simulated catalogues, describe the procedure, and characterize the results. We find the distribution of the length of the filaments, and suggest how to use this approach to obtain other statistical characteristics of filamentary networks.