检测加权网络块结构的持久同调方法
Persistent homology method to detect block structures in weighted networks
摘要：
解开网络的块结构对于研究宏观特征和社区层面的动态至关重要。加权随机块模型（WSBM）是传统随机块模型的一种变体，它是为加权网络设计的，但它并不总是最优的。本文介绍了一种新的拓扑方法，通过比较加权网络的持久图来研究加权网络的块结构。我们发现不同块结构的网络的持久性图显示出不同的特征，足以区分。此外，即使使用更多随机示例或修改的超参数，也可以保留整体特征。最后，当测试潜块结构未知的随机图时，持久性图分析的结果与其加权随机块模型一致。虽然由于某些原因，这种拓扑方法不能完全取代原来的WSBM方法，但值得进一步研究。
英文摘要：
Unravelling the block structure of a network is critical for studying macroscopic features and community-level dynamics. The weighted stochastic block model (WSBM), a variation of the traditional stochastic block model, is designed for weighted networks, but it is not always optimal. We introduce a novel topological method to study the block structure of weighted networks by comparing their persistence diagrams. We found persistence diagrams of networks with different block structures show distinct features, sufficient to distinguish. Moreover, the overall characteristics are preserved even with more stochastic examples or modified hyperparameters. Finally, when random graphs whose latent block structure is unknown are tested, results from persistence diagram analysis are consistent with their weighted stochastic block model. Although this topological method cannot completely replace the original WSBM method for some reasons, it is worth to be investigated further.
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