HODs as a function of halo mass for groups at different proximity thresholds. Upper panels: HODs for subsamples within 25% (cyan), 15% (orange), and 5% (violet) of the nearest global maxima (left), global minima (center), and DisPerSE skeleton (right), compared to the complete sample (dashed black line). Lower panels: Ratios of each sample HOD to the complete sample HOD. The larger fluctuations at high masses reflect the smaller number of halos in these regimes. Error bars represent jackknife uncertainties estimated using 100 spatial subsamples. All results correspond to the absolute magnitude cut M_r < −20.0.