  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
B3-spline kernel of the radius of 8 Mpc/h for the main sample and 16 Mpc/h 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.
