Methodological study demonstrates consistent graph covariance estimation in latent position random graphs, providing a robust framework for testing network independence.
Key Points
To develop a mathematical framework for measuring correlation and testing statistical independence between two latent position random graphs where underlying positions are unobservable.
Formulated a correlation coefficient in reproducing kernel Hilbert space (RKHS) based on the spectral decomposition of network adjacency matrices.
Developed a non-parametric permutation procedure to test independence between paired random graphs.
Extended the formulation to spectral decompositions of normalized Laplacian matrices for inhomogeneous random graphs and validated with simulations and real-world data.
Demonstrated that sample graph covariance consistently converges in probability to its population counterpart even without specifying an explicit kernel function.
Confirmed the statistical power and validity of the proposed permutation test in detecting graph dependence across simulated scenarios and empirical datasets.