Abstract
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 [Formula: see text] is below a critical value [Formula: see text] For covalent polymer networks, increasing the network size, as measured by the number of cross-link nodes, beyond [Formula: see text] results in a crossover to a new regime in which the characteristic size of the chordless cycles [Formula: see text] no longer increases. From this result, the onset and intensity of finite-size effects can be predicted from measurement of [Formula: see text] 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.
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