  To understand the formation and evolution of massive cosmic structures,
studying them at high redshift, in the epoch when they formed the majority of
their mass is essential. The One-hundred-deg$^2$ DECam Imaging in Narrowbands
(ODIN) survey is undertaking the widest-area narrowband program to date, to use
Ly$\alpha$-emitting galaxies (LAEs) to trace the large-scale structure (LSS) of
the Universe at three cosmic epochs. In this work, we present results at $z$ =
3.1 based on early ODIN data in the COSMOS field. We identify and characterize
protoclusters and cosmic filaments using multiple methods and discuss their
strengths and weaknesses. We then compare our observations against the
IllustrisTNG suite of cosmological hydrodynamical simulations. The two are in
excellent agreement, with a similar number and angular size of structures
identified above a specified density threshold. We are able to recover the
simulated protoclusters with $\log$(M$_{z=0}$/$M_\odot$) $\gtrsim$ 14.4 in
$\sim$ 60\% of the cases. With these objects we show that the descendant masses
of the protoclusters in our sample can be estimated purely based on our 2D
measurements, finding a median $z$ = 0 mass of $\sim10^{14.5}$M$_\odot$. The
lack of information on the radial extent of each protocluster introduces a
$\sim$0.4~dex uncertainty in its descendant mass. Finally, we show that the
recovery of the cosmic web in the vicinity of protoclusters is both efficient
and accurate. The similarity of our observations and the simulations imply that
our structure selection is likewise robust and efficient, demonstrating that
LAEs are reliable tracers of the LSS.
