Steps for computing a radial filament profile. Black dots: represent the extremities of a filament segment, given by DisPerSE. They are connected by black straight lines, constituting the filament spine. The gray area illustrates the area within 25 Mpc from the filament spine, where data from the tSZ or lensing map are used. For example, blue points are some data points on the tSZ or lensing map that we used to construct a radial profile. These are attached to the closest positions of the filament spine to calculate the radial distances. The radial profile is calculated based on a grid coordinate in physical distance up to 25 Mpc, divided into 20 bins (such as in Fig. 5). Data in masked regions (white disks) are not used in the analysis.