The dependency of atomic and molecular content at fixed halo mass for galaxies inside and outside filaments. Top: HI-deficiency as a function of the host halo mass M_halo in GAEA-all. Colour coding reflects the position concerning filaments: inside or outside. Big circles show median values with 1σ confidential interval for galaxies inside and outside filaments in each mass bin (median values were estimated for similar M_halo distribution for haloes inside and outside filaments by bootstrapping). On the background, typical pure filament/pure field (90%-quantile) and clusters of halo masses are highlighted. Bottom: Same but for H₂-deficiency.