Distribution and cross correlation of several halo properties used in this work. Each row/column corresponds to a specific quantity. The rightmost panel of every row displays the probability distribution of that quantity, while the other panels represent the cross correlation between different pairs of quantities. From left to right: halo mass (M_200c), relaxedness parameter based on distance, relaxedness parameter based on mass, formation redshift, SMBH mass, and SMBH accretion rate. Each dot corresponds to an individual galaxy cluster.