For inhomogeneous random graphs with a graphon variance profile, the traces of powers of the adjacency matrix, suitably rescaled, converge to Gaussian processes with covariances expressible as graphon homomorphism densities.
An introduction to random matrices , volume 118
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Central limit theorems for linear spectral statistics of inhomogeneous random graphs with graphon limits
For inhomogeneous random graphs with a graphon variance profile, the traces of powers of the adjacency matrix, suitably rescaled, converge to Gaussian processes with covariances expressible as graphon homomorphism densities.