Left and middle panels: histograms of the luminosity concentration (left) and the offset between the BCG and X-ray flux-weighted centroid (middle) of all 64 HIFLUGCS clusters with their Gaussian fits shown as solid curves. The mean of the Gaussian fits and their 1σ clipping are shown as dashed and solid vertical lines, respectively. Right panel: c_L versus ΔR/r₅₀₀ with its best fit, log ₁₀c_L = (0.593 ± 0.053) + (0.125 ± 0.028)log ₁₀(ΔR/r₅₀₀), as dash-dotted line. The vertical and horizontal solid lines denote the 1σ clipping below which the clusters are considered as undisturbed ones (open squares). The disturbed clusters are shown as open triangles.