  We applied a Density-Based Clustering algorithm on samples of galaxies and
galaxy systems belonging to 53 rich superclusters from the \textit{Main
SuperCluster Catalogue} (MSCC) to identify the presence of ``central regions'',
or \emph{cores}, in these large-scale structures. \emph{Cores} are defined here
as large gravitationally bound galaxy structures, comprised of two or more
clusters and groups, with sufficient matter density to survive cosmic expansion
and virialize in the future. We identified a total of 105 galaxy structures
classified as \emph{cores}, which exhibit a high density contrast of mass and
galaxies. The Density-based \textit{Core} Catalogue (DCC), presented here,
includes \emph{cores} that were previously reported in well-known superclusters
of the Local Universe, and also several newly identified ones. We found that
83\% of the rich superclusters in our sample have at least one \emph{core}.
While more than three \emph{cores} with different dynamical state are possible,
the presence of a single \emph{core} in the superclusters is more common. Our
work confirms the existence of nucleation regions in the internal structure of
most rich superclusters and points to the fact that these \emph{cores} are the
densest and most massive features that can be identified in the cosmic web with
high probability for future virialization.
