  In 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 halos 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 (MST) and the Friends of Friends (FoF) 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 halos 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.
