  We study the effect of baryons on the cosmic web -- halos, filaments, walls,
and voids. To do so, we apply a modified version of NEXUS, a cosmic web
morphological analysis algorithm, to the IllustrisTNG simulations. We find that
halos lose more than $10\%$ of their mass due to baryons, mostly to filaments
and a small portion to walls and voids. However, the mass transfer does not
significantly shift the boundaries of structures, leaving the volume fractions
of the cosmic structures largely unaffected. We quantify the effects of
baryonic feedback on the power spectrum and the probability density function
(PDF) of the density field for individual cosmic structures. For the power
spectrum, most suppression due to feedback can be accounted for by including
$M\ge10^{12}~M_\odot/h$ halos, without considering other cosmic structures.
However, when examining the PDF of the density field, we find nearly $100\%$
suppression of the emptiest regions and $10\%$-level effects (boost or
suppression) in the remaining regions of filaments, walls, and voids. Our
results indicate the importance of modeling the effects of baryons in the whole
cosmic web, not just halos, for cosmological analysis beyond two-point
statistics or field-based inferences.
