Abstract: The talk considers the multilayer  network model, introduced in Pensky and Wang (2021), where all layers of the network have the same collection of nodes and are equipped with the Stochastic Block Models. In addition, all layers can be partitioned into groups with the same community structures, although the layers in the same group may have different matrices of block connection probabilities.

The model generalizes a multitude of papers that study multilayer networks where the same community structure persists in all layers, as well as the Mixture Multilayer Stochastic Block Model, where the layers in the same group have identical matrices of block connection probabilities.