Radial profiles of the gas inflow (left column) and gas outflow (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 represents a different halo mass bin. The thick solid lines illustrate the mean profile, while the thin lines represent individual clusters. The figure underscores the significant impact of halo properties on gas inflow and outflow.