  This paper proposes a multilayer graph model for the community detection from
multiple observations. This is a very frequent situation, when different
estimators are applied to infer graph edges from signals at its nodes, or when
different signal measurements are carried out. The multilayer network stacks
the graph observations at the different layers, and it links replica nodes at
adjacent layers. This configuration matches the Cartesian product between the
ground truth graph and a path graph, where the number of nodes corresponds to
the number of the observations. Stemming on the algebraic structure of the
Laplacian of the Cartesian multilayer network, we infer a subset of the
eigenvectors of the true graph and perform community detection. Experimental
results on synthetic graphs prove the accuracy of the method, which outperforms
state-of-the-art approaches in terms of ability of correctly detecting graph
communities. Finally, we show the application of our method to discriminate
different brain networks derived from real EEG data collected during motor
imagery experiments. We conclude that our approach appears promising in
identifying graph communities when multiple observations of the graph are
available and it results promising for EEG-based motor imagery applications.
