Cool core criteria as a function of M_500c for the entire TNG-Cluster sample at z = 0. The color of the symbols indicates whether the clusters are classified as SCC (dark blue dots), WCC (purple crosses), or NCC (orange diamonds) according to the quantity on the y-axis. The black line shows the median trend of the CC criteria with M_500c. The silver solid region shows the 16 to 84 percentile ranges. From upper left to lower right: central cooling time, central electron number density, central entropy, physical concentration parameter, scaled concentration parameter, and cuspiness parameter. We also made qualitative, face value-only comparisons to values from selected nearby clusters (see text). Overall, there is no well-defined mass trend visible across all CC criteria. In some cases, the central cluster properties do not depend on mass, while other properties show increasing, decreasing, or non-monotonic behavior with halo mass. The number of SCC cluster varies substantially depending on the defining criteria.