We present a statistical study of the filamentary structures of the cosmic web in the large hydro-dynamical simulations Illustris-TNG, Illustris, and Magneticum at redshift z = 0. We focus on the radial distribution of the galaxy density around filaments detected using the Discrete Persistent Structure Extractor (DisPerSE). We show that the average profile of filaments presents an excess of galaxy density (> 5σ) up to radial distances of 27 Mpc from the core. The relation between galaxy density and the length of filaments is further investigated showing that short (Lf <  9 Mpc) and long (Lf ≥ 20 Mpc) filaments are two statistically different populations. Short filaments are puffier, denser, and more connected to massive objects, whereas long filaments are thinner, less dense, and more connected to less massive structures. These two populations trace different environments and may correspond to bridges of matter between over-dense structures (short filaments), and to cosmic filaments shaping the skeleton of the cosmic web (long filaments). Through Markov chain Monte Carlo (MCMC) explorations, we find that the density profiles of both short and long filaments can be described by the same empirical models (generalised Navarro, Frenk and White, β-model, a single and a double power law) with different and distinct sets of parameters.

Galaxy clusters are connected at their peripheries to the large scale structures by cosmic filaments that funnel accreting material. These filamentary structures are studied to investigate both environment-driven galaxy evolution and structure formation and evolution. In the present work, we probe in a statistical manner the azimuthal distribution of galaxies around clusters as a function of the cluster-centric distance, the cluster richness, and the galaxy activity (star-forming or passive). We perform a harmonic decomposition in large photometric galaxy catalogue around 6400 SDSS clusters with masses M > 10 14 solar masses, in the redshift range of 0.1 < z < 0.3. The same analysis is performed on the mock galaxy catalogue from the light-cone of Magneticum hydrodynamical simulation. We use the multipole analysis to quantify asymmetries in the 2-D galaxy distribution. In the inner cluster regions at R < 2R500, we confirm that the galaxy distribution traces an ellipsoidal shape, which is more pronounced for richest clusters. In the clusters' outskirts (R = [2 − 8]R500), filamentary patterns are detected in harmonic space with a mean angular scale mmean = 4.2 ± 0.1. Massive clusters seem to have a larger number of connected filaments than low massive ones. We also find that passive galaxies appear to better trace the filamentary structures around clusters, even if the contribution of SF ones tend to increase with the cluster-centric distance, suggesting a gradient of galaxy activity in filaments around clusters.