The work in this paper provides evidence for temporal brain dynamics during resting state through dynamic multi-layer community detection which enables us to better understand the behavior of different subnetworks.

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Modern data analysis and processing tasks typically involve large sets of structured data, where the structure carries critical information about the nature of the data. Graphs provide a powerful tool to describe the structure of such data. In particular, entities and the relationships between them are modeled as the nodes and edges of the graph, respectively. Traditional single layer network models are insufficient for describing the multiple entity types and modes of interaction encountered in real-world applications. Recently, multi-layer network models, where the different types of interactions are captured by layers, have emerged to model these systems. These networks consider the relationships between nodes both within layers, i.e., intra-layer edges, and across layers, i.e., inter-layer edges. One of the important tools in understanding the topology of these high-dimensional networks is community detection. In this paper, a joint nonnegative matrix factorization approach is proposed to detect the community structure in multi-layer networks. The proposed approach detects the intra-and inter-layer community structures, simultaneously. The performance of the proposed approach is evaluated for both simulated and real networks.

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