Section: New Results

Minimax estimation of network complexity in graphon model

In network analysis, the graphon model has attracted a lot of attention as a non-parametric model with some universal properties. However, this approach suffers from interpretability and identifiability issues in practice. A first solution to this problem was obtained by Y. Issartel: he introduces an identifiable and interpretable functional of the graphon, which measures the complexity of network [25]. It has simple interpretations on popular examples of random graphs: it matches the number of communities in stochastic block models; the dimension of the Euclidean space in random geometric graphs; the regularity of the link function in Hölder graphons. He also provides an estimation procedure of this complexity that is minimax optimal.