Percolation and cluster structure parameters: The radius of gyration

The squared radius of gyration of percolation clusters are determined in terms of the clusters' second spatial moments using the enhanced Hoshen-Kopelman algorithm for square and triangular lattices containing 2.025 x 10(9) sites. Correlation length exponents and related exponents as well as their corresponding amplitudes are calculated in terms of the squared radius of gyration above and below the percolation threshold. A coefficient for cluster compactness that is based on the squared radius of gyration of a cluster is introduced. That coefficient is compared with a similar coefficient of compactness that is based on the cluster cyclomatic number.