Distribution of azimuthal symmetric excess β (as defined in Eq. (12)) computed at cluster peripheries in (1 <  R[R₂₀₀]< 2) as a function of the halo connectivity, for DM (black) and WHIM (orange). The mean profiles of β and their errors are shown as solid lines. The number of objects used to compute the average in each bin of the x-axis (shown with grey dotted lines) is written above the figures in grey.