  Objective: In recent years, the functional connectivity of the human brain
has been studied with graph theoretical tools. One such approach is community
detection which is fundamental for uncovering the localized networks. Existing
methods focus on networks constructed from a single frequency band while
ignoring multi-frequency nature of functional connectivity. Therefore, there is
a need to study multi-frequency functional connectivity to be able to capture
the full view of neuronal connectivity. Methods: In this paper, we use
multilayer networks to model multi-frequency functional connectivity. In the
proposed model, each layer corresponds to a different frequency band. We then
extend the definition of modularity to multilayer networks to develop a new
community detection algorithm. Results} The proposed approach is applied to
electroencephalogram data collected during a study of error monitoring in the
human brain. The differences between the community structures within and across
different frequency bands for two response types, i.e. error and correct, are
studied. Conclusion: The results indicate that following an error response, the
brain organizes itself to form communities across frequencies, in particular
between theta and gamma bands while a similar cross-frequency community
formation is not observed for the correct response. Moreover, the community
structures detected for the error response were more consistent across subjects
compared to the community structures for correct response. Significance: The
multi-frequency functional connectivity network models combined with multilayer
community detection algorithms can reveal changes in cross-frequency functional
connectivity network formation across different tasks and response types.
