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Abstract:
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Much of the focus of statistical works on networks has been on static networks, multiple networks are currently becoming more common among network data sets. Usually, a number of network data sets, which share some form of connection between each other are known as multiple or multi-layer networks. We consider the problem of identifying the common and dynamic community structures for multiple networks. We propose a class of network models for multiple networks. We consider extensions of the spectral clustering methods for the multiple network models, and give theoretical guarantee that the spectral clustering methods produce consistent community detection in case of both multiple stochastic block model and multiple degree-corrected block models. The methods are shown to work under sufficiently mild conditions on the number of multiple networks to detect associative, dissociative and mixed community structures, even if all the individual networks are very sparse and most of the individual networks are below community detectability threshold. We reinforce the validity of the theoretical results via simulations too.
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