  Despite numerous studies, the relationship between network structure and
fracture remains unclear. In this study, the fracture properties of end-linking
networks were compared with those of loop-free analogs made from star
prepolymers by performing phantom chain simulations. The networks were created
from equilibrated sols of stoichiometric mixtures of linear prepolymers and
f-functional linkers through end-linking reactions using Brownian dynamics
schemes. The examined networks, with various f values (between 3 and 8) and
strand-connection rates ({\phi}_s), were evaluated in terms of the primary loop
fraction and the cycle rank {\xi}. These structural characteristics were
consistent with mean-field theories that assume independent reactions. Energy
minimization and uniaxial stretch were applied to the networks until they broke
without Brownian motion. The fracture characteristics, including strain
({\epsilon}_b), stress ({\sigma}_b), and work for fracture (W_b), were obtained
from stress-strain curves. The end-linking networks exhibited larger
{\epsilon}_b and smaller {\sigma}_b and W_b than those for star networks due to
primary loops, at the same set of f and {\phi}_s. However, {\epsilon}_b,
{\sigma}_b/{\nu}_br and W_b/{\nu}_br (with {\nu}_br being the branch point
density) lie on the same master curves as those for star networks if they are
plotted against {\xi}. This result implies that the fracture of end-linking
networks is essentially the same as that for star analogs, and the effects of
primary loops are embedded in {\xi}.
