We consider community detection from multiple correlated graphs sharing the same community structure. The correlated graphs are generated by independent subsampling of a parent graph sampled from the stochastic block model. The vertex correspondence between the correlated graphs is assumed to be unknown. We consider the two-step procedure where the vertex correspondence between the correlated graphs is first revealed, and the communities are recovered from the union of the correlated graphs, which becomes denser than each single graph. We derive the information-theoretic limits for exact graph matching in general density regimes and the number of communities, and then analyze the regime of graph parameters, where one can benefit from the matching of the correlated graphs in recovering the latent community structure of the graphs.

翻译：我们考虑从多个共享相同社区结构的相关图中进行社区检测。这些相关图通过对从随机块模型中采样的父图进行独立子采样生成。相关图之间的顶点对应关系被假设为未知。我们采用两步流程：首先揭示相关图之间的顶点对应关系，然后从相关图的并集中恢复社区结构，该并集比每个单一图更为稠密。我们推导了一般密度区域和社区数量下精确图匹配的信息论极限，并分析了图参数的区间，在该区间内，可以通过相关图的匹配来恢复图的潜在社区结构。