a) 8 h-1 Mpc smoothed luminosity density distribution of groups inside (blue) and outside (light red) of filaments in M 20 volume-limited sample. Purple color represents overlapping distribution. b) Mean perpendicular distances of central galaxies outside of filaments measured from the filament axes plotted as a function of group masses in different environments defined by the luminosity density field. c) Mean length of filaments as a function of group masses in different environments within filaments. d) Mean distances of central galaxies along the filament axes as a function of group masses in different environments defined by the luminosity density field.
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