LAUSR

The chordless cycle sizes of spatially embedded networks are demonstrated to follow an exponential growth law similar to random graphs if the number of nodes Nx is below a critical value N*. For covalent polymer networks, increasing the network size, as measured by the number of cross-link nodes, beyond N* results in a crossover to a new regime in which the characteristic size of the chordless cycles h* no longer increases. From this result, the onset and intensity of finite-size effects can be predicted from measurement of h* in large networks. Although such information is largely inaccessible with experiments, the agreement of simulation results from molecular dynamics, Metropolis Monte Carlo, and kinetic Monte Carlo suggests the crossover is a fundamental physical feature which is insensitive to the details of the network generation. These results show random graphs as a promising model to capture structural differences in confined physical networks.