Characterising HOD in filaments and nodes of the cosmic web

The standard paradigm for the formation of the Universe suggests that large structures are formed from hierarchical clustering by the continuous accretion of less massive galaxy systems through filaments. In this context, filamentary structures play an important role in the properties and evolution of galaxies by connecting high-density regions, such as nodes, and being surrounded by low-density regions, such as cosmic voids. The availability of the filament and point critic catalogues extracted by \textsc{DisPerSE} from the \textsc{Illustris} TNG300-1 hydrodynamic simulation allows a detailed analysis of these structures. The halo occupation distribution (HOD) is a powerful tool for linking galaxies and dark matter halos, allowing constrained models of galaxy formation and evolution. In this work we combine the advantage of halo occupancy with information from the filament network to analyse the HOD in filaments and nodes. In our study, we distinguish the inner regions of cosmic filaments and nodes from their surroundings. The results show that the filamentary structures have a similar trend to the total galaxy sample covering a wide range of densities. In the case of the nodes sample, an excess of faint and blue galaxies is found for the low-mass nodes suggesting that these structures are not virialised and that galaxies may be continuously falling through the filaments. Instead, the higher-mass halos could be in a more advanced stage of evolution showing features of virialised structures.