Radial profiles of the inflowing gas radial velocity (left column) and the outflowing gas radial velocity (right column) for halos classified based on their relaxedness (first row), formation time (second row), SMBH mass (third row), and SMBH accretion rate (fourth row). Each color corresponds to a different halo mass bin. The thick solid lines depict the mean profile, while the thin lines represent individual clusters. The figure emphasizes the significant correlations between halo properties and the kinematics of gas.