Distance between our clusters and the nearest filament as a function of their X-ray surface brightness SB_X. The figure is colour-coded according to the X-ray surface brightness: high surface brightness clusters are shown with red circles, low surface brightness with blue squares, and intermediate cases with black stars. The farthest object in our sample is highlighted with a blue open square, and it refers to CL1011, a peculiar case that we analyse in detail in Appendix A.