The extended ROSAT-ESO Flux Limited X-ray Galaxy Cluster Survey (REFLEX
  II) III. Construction of the first flux-limited supercluster sample
  We present the first supercluster catalogue constructed with the extended
ROSAT-ESO Flux Limited X-ray Galaxy Cluster survey (REFLEX II) data, which
comprises 919 X-ray selected galaxy clusters. Based on this cluster catalogue
we construct a supercluster catalogue using a friends-of-friends algorithm with
a linking length depending on the local cluster density. The resulting
catalogue comprises 164 superclusters at redshift z<=0.4. We study the
properties of different catalogues such as the distributions of the redshift,
extent and multiplicity by varying the choice of parameters. In addition to the
main catalogue we compile a large volume-limited cluster sample to investigate
the statistics of the superclusters. We also compare the X-ray luminosity
function for the clusters in superclusters with that for the field clusters
with the flux- and volume-limited catalogues. The results mildly support the
theoretical suggestion of a top-heavy X-ray luminosity function of galaxy
clusters in regions of high cluster density.
