Hidden community is a new graph-theoretical concept recently proposed [4], in which the authors also propose a meta-approach called HICODE (Hidden Community Detection) for detecting hidden communities. HICODE is demonstrated through experiments that it is able to uncover previously overshadowed weak layers and uncover both weak and strong layers at a higher accuracy. However, the authors provide no theoretical guarantee for the performance. In this work, we focus on the theoretical analysis of HICODE on synthetic two-layer networks, where layers are independent of each other and each layer is generated by stochastic block model. We bridge their gap through two-layer stochastic block model networks in the following aspects: 1) we show that partitions that locally optimize modularity correspond to grounded layers, indicating modularity-optimizing algorithms can detect strong layers; 2) we prove that when reducing found layers, HICODE increases absolute modularities of all unreduced layers, showing its layer reduction step makes weak layers more detectable. Our work builds a solid theoretical base for HICODE, demonstrating that it is promising in uncovering both weak and strong layers of communities in two-layer networks.

中文翻译：

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两层随机模型上的隐藏社区检测：理论视角

隐藏社区是最近提出的一个新的图论概念 [4]，其中作者还提出了一种称为 HICODE（隐藏社区检测）的元方法来检测隐藏社区。HICODE 通过实验证明，它能够发现先前被遮蔽的弱层，并以更高的精度同时发现弱层和强层。但是，作者没有为性能提供理论保证。在这项工作中，我们专注于 HICODE 在合成两层网络上的理论分析，其中层彼此独立，每层由随机块模型生成。我们在以下方面通过两层随机块模型网络弥合了它们的差距：1）我们表明局部优化模块化的分区对应于接地层，指示模块化优化算法可以检测强层；2）我们证明，当减少找到的层时，HICODE增加了所有未减少层的绝对模块性，表明其层减少步骤使弱层更易于检测。我们的工作为 HICODE 建立了坚实的理论基础，表明它在揭示两层网络中社区的弱层和强层方面很有前景。