  In this work, we introduce a predictive approach for determining fracture
nucleation in thermosets based on shortest paths (SPs) of the network topology.
This method enumerates SP sets in networks with periodic boundary conditions,
with applications to both all-atom and coarse-grained simulations. We find that
network fracture is most likely to nucleate on the first (shortest) SP and the
strain at nucleation is linearly correlated with the topological path length.
Subsequent fracture events are dictated by the instantaneous SP of partially
broken networks. We further quantify the length scale dependence of SP
distributions, introducing a means of bridging simulated and experimental
fracture profiles.
