Averages of unlabeled networks: geometric characterization and asymptotic behavior (Q2176631)

Considering the setting where observed data comes in the form of networks, the authors develop tools to allow fundamental statistical analysis in the case of unlabeled, undirected graphs with weighted edges. In particular, they formulate the class of such graphs, investigate geometric and topological aspects of this class, and develop appropriate averages, based on Fréchet means, which can be used when sampling from a distribution supported on this space (together with a corresponding law of large numbers and central limit theorem).