The effect of cross-linker functionality and interfacial bond density on the fracture behavior of highly cross-linked polymer networks bonded to a solid surface is studied using large-scale molecular dynamics simulations. Three different cross-linker functionalities (f = 3, 4, and 6) are considered. The polymer networks are created between two solid surfaces with the number of bonds to the surfaces varying from zero to full bonding to the network. Stress-strain curves are determined for each system from tensile pull and shear deformations. At full interfacial bond density the failure mode is cohesive. The cohesive failure stress is almost identical for shear and tensile modes. The simulations directly show that cohesive failure occurs when the number of interfacial bonds is greater than in the bulk. Decreasing the number of interfacial bonds results in cohesive to adhesive transition consistent with recent experimental results. The correspondence between the stress-strain curves at different f and the sequence of molecular deformations is obtained. The failure stress decreases with smaller f while failure strain increases with smaller f.