Efficient algorithm for primitive ring statistics in topological networks

An efficient algorithm for finding primitive rings in a topological network has been developed. The calculation of complete ring statistics, with virtually no upper limit on ring size, becomes feasible for very large network systems. The computing time and memory usage are vastly reduced by utilizing the primitive ring properties and a four-point directing method. Various ring definitions are also discussed and analyzed in detail. Finally, examples are provided for analyzing alkali-rich regions in silicate glasses using ring statistics up to 33-membered primitive rings, obtained by this algorithm.