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For graph-valued data sampled iid from a distribution $\mu$, the samplemoments are computed with respect to a choice of metric. In this work, we equipthe set of graphs with the pseudo-metric defined by the $\ell_2$ norm betweenthe eigenvalues of the respective adjacency matrices. We use this pseudo metricand the respective sample moments of a graph valued data set to infer theparameters of a distribution $\hat{\mu}$ and interpret this distribution as anapproximation of $\mu$. We verify experimentally that complex distributions$\mu$ can be approximated well taking this approach.

Probability density estimation for sets of large graphs with respect to spectral information using stochastic block models