  The paper introduces the DIverse MultiPLEx Generalized Dot Product Graph
(DIMPLE-GDPG) network model where all layers of the network have the same
collection of nodes and follow the Generalized Dot Product Graph (GDPG) model.
In addition, all layers can be partitioned into groups such that the layers in
the same group are embedded in the same ambient subspace but otherwise all
matrices of connection probabilities can be different. In a common particular
case, where layers of the network follow the Stochastic Block Model (SBM), this
setting implies that the groups of layers have common community structures but
all matrices of block connection probabilities can be different. We refer to
this version as the DIMPLE model. While the DIMPLE-GDPG model generalizes the
COmmon Subspace Independent Edge (COSIE) random graph model developed in
\cite{JMLR:v22:19-558}, the DIMPLE model includes a wide variety of
SBM-equipped multilayer network models as its particular cases. In the paper,
we introduce novel algorithms for the recovery of similar groups of layers, for
the estimation of the ambient subspaces in the groups of layers in the
DIMPLE-GDPG setting, and for the within-layer clustering in the case of the
DIMPLE model. We study the accuracy of those algorithms, both theoretically and
via computer simulations. The advantages of the new models are demonstrated
using real data examples.
