  We study the evolution of the Halo Occupation Distribution (HOD) and galaxy
properties of nodes and filamentary structures obtained by DisPerSE from the
Illustris TNG300-1 hydrodynamical simulation, in the redshift range $0 \leq z
\leq 2$. We compute the HOD in filaments and nodes and fit the HOD parameters
to study their evolution, taking into account both faint and bright galaxies.
In nodes, the number of faint galaxies increases with the decreasing redshift
in the low-mass halos, while no significant differences are seen in the
high-mass halos. Limiting the HOD to bright galaxies shows that the halos
increase in mass more than the number of bright galaxies they accrete. For
filaments, no large differences in HOD are found for faint galaxies, although
for brighter galaxies the behaviour is similar to that for nodes. The HOD
parametrization suggests that filaments have no effect on the mass required to
host a galaxy (central or satellite), whereas nodes do. The results of the
study indicate that filaments do not seem to affect the stellar mass content of
galaxies. In contrast, nodes appear to affect halos with masses below
approximately $10^{12.5} h^{-1} M_{\odot}$ at local redshift. The analysis of
the galaxy colour evolution shows a reddening towards lower redshift, although
these processes seem to be more efficient in massive halos, with a strong
effect on the bright galaxies. The general evolution suggests that the building
of galaxy population within halos is influenced by both the accretion of faint
galaxies and the mass growth of the bright ones.
