The network geometries of rigidly cross-linked fibrin and collagen type I networks are imaged using confocal microscopy and characterized statistically. This statistical representation allows for the regeneration of large, three-dimensional biopolymer networks using an inverse method. Finite element analyses with beam networks are then used to investigate the large deformation, nonlinear elastic response of these artificial networks in isotropic stretching and simple shear. For simple shear, we investigate the differential bulk modulus, which displays three regimes: a linear elastic regime dominated by filament bending, a regime of strain-stiffening associated with a transition from filament bending to stretching, and a regime of weaker strain-stiffening at large deformations, governed by filament stretching convolved with the geometrical nonlinearity of the simple shear strain tensor. The differential bulk modulus exhibits a corresponding strain-stiffening, but reaches a distinct plateau at about 5\,% strain under isotropic stretch conditions. The small-strain moduli, the bulk modulus in particular, show a significant size-dependence up to a network size of about 100 mesh sizes. The large-strain differential shear modulus and bulk modulus show very little size-dependence.