  We investigate the impact of the number of filaments connected to the nodes
of the cosmic web on the physical properties of their galaxies using the Sloan
Digital Sky Survey. We compare these measurements to the cosmological
hydrodynamical simulations Horizon-(no)AGN and Simba. We find that more massive
galaxies are more connected, in qualitative agreement with theoretical
predictions and measurements in dark matter only simulation. The star formation
activity and morphology of observed galaxies both display some dependence on
the connectivity of the cosmic web at fixed stellar mass: less star forming and
less rotation supported galaxies also tend to have higher connectivity. These
results qualitatively hold both for observed and virtual galaxies, and can be
understood given that the cosmic web is the main source of fuel for galaxy
growth. The simulations show the same trends at fixed halo mass, suggesting
that the geometry of filamentary infall impacts galaxy properties beyond the
depth of the local potential well. Based on simulations, it is also found that
AGN feedback is key in reversing the relationship between stellar mass and
connectivity at fixed halo mass. Technically, connectivity is a practical
observational proxy for past and present accretion (minor mergers or diffuse
infall).
