The equilibrium structure of supramolecular magnetic filament brushes is analyzed at two different scales. First, we study the density and height distributions for brushes with various grafting densities and chain lengths. We use Langevin dynamics simulations with a bead-spring model that takes into account the cross-links between the surface of the ferromagnetic particles, whose magnetization is characterized by a point dipole. Magnetic filament brushes are shown to be more compact near the substrate than nonmagnetic ones, with a bimodal height distribution for large grafting densities. This latter feature makes them also different from brushes with electric dipoles. Next, in order to explain the observed behavior at the filament scale, we introduce a graph theory analysis to elucidate for the first time the structure of the brush at the scale of individual beads. It turns out that, in contrast to nonmagnetic brushes, in which the internal structure is determined by random density fluctuations, magnetic forces introduce a certain order in the system. Because of their highly directional nature, magnetic dipolar interactions prevent some of the random connections to be formed. On the other hand, they favor a higher connectivity of the chains' free and grafted ends. We show that this complex dipolar brush microstructure has a strong impact on the magnetic response of the brush, as any weak applied field has to compete with the dipole-dipole interactions within the crowded environment.