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

For graph-valued data sampled iid from a distribution $μ$, the sample moments are computed with respect to a choice of metric. In this work, we equip the set of graphs with the pseudo-metric defined by the $\ell_2$ norm between the eigenvalues of the respective adjacency matrices. We use this pseudo metric and the respective sample moments of a graph valued data set to infer the parameters of a distribution $\hatμ$ and interpret this distribution as an approximation of $μ$. We verify experimentally that complex distributions $μ$ can be approximated well taking this approach.