ABSTRACTIn this work, we identify and analyse the properties of cluster–cluster filaments within a cosmological simulation assuming that they are structures connecting maxima of the density field defined by dark matter haloes with masses $M \, \ge 10^{14}\, h^{-1} \, \mathrm{M_{\odot }}$. To extract these filaments we develop an identification algorithm based on two standard tools: the Minimal Spanning Tree and the friends-of-friends algorithm. Focusing our analysis on the densest dark matter filaments, we found that the radial density profile, at scales around $1\, h^{-1} \, \mathrm{Mpc}$, approximately follow a power-law function with index −2. Without making any assumption about the velocity field, our algorithm finds that the saddle point arises as a natural characteristic of the filamentary structure. In addition, its location along the filament depends on the masses of the haloes at the filament ends. We also found that the infall velocities follow a cross-pattern near the saddle point, being perpendicular to the filament spine when approaching from low-density regions, and parallel away from the saddle point towards the ends of the filament. Following theoretical prescriptions, we estimate the linear density from the transverse velocity dispersion, finding a good correspondence with the measured mass per unit length of our filaments. Our results can be applied to observational samples of filaments in order to link the saddle point location and the mass per unit length with measurements obtained from observations such as cluster masses and the velocity dispersion of galaxies.