Coarse-grained molecular dynamics (MD) simulations are applied to fracture in highly cross-linked, polymer networks. Random polymer networks between two solid surfaces are created by simulating the dynamical cross-linking process. Simple, ordered networks are constructed geometrically, which enables easy manipulation of the network connectivity. The failure strain of tensile pull and shear simulations is related to the minimal paths through the network connecting the solid surfaces. This result is confirmed by using the ordered networks to explicity vary the minimal paths over a very wide range. Failure strains are constructed in the ordered systems to be either larger or smaller than the dynamically formed networks. The constraints imposed by the network connectivity control the tightness of local deformations.