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.

中文翻译：

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多频脑电网络中的社区检测

目的：近年来，利用图论工具对人脑的功能连通性进行了研究。一种这样的方法是社区检测，它是发现本地网络的基础。现有方法侧重于从单个频带构建的网络，而忽略了功能连接的多频特性。因此，有必要研究多频功能连接，以便能够捕捉到神经元连接的全貌。方法：在本文中，我们使用多层网络对多频功能连接进行建模。在所提出的模型中，每一层对应一个不同的频带。然后，我们将模块化的定义扩展到多层网络，以开发一种新的社区检测算法。结果} 所提出的方法适用于在人脑错误监测研究期间收集的脑电图数据。研究了两种响应类型（即错误和正确）在不同频段内和跨频段的社区结构之间的差异。结论：结果表明，在错误响应之后，大脑组织自己形成跨频率的社区，特别是在 theta 和 gamma 波段之间，而对于正确的响应，没有观察到类似的跨频率社区形成。此外，与正确响应的社区结构相比，针对错误响应检测到的社区结构在受试者之间更加一致。意义：