The user alignment of cross-social networks is divided into user and group alignments, respectively. Obtaining users' full features is difficult due to social network privacy protection policies in user alignment mode. In contrast, the alignment accuracy is low due to the large number of edge users in the group alignment mode. To resolve this issue, First, stable topics are obtained from user-generated content (UGC) based on embedded topic jitter time, and the weight of user edges is updated by using vector distances. An improved Louvain algorithm, called Stable Topic-Louvain (ST-L), is designed to accomplish multi-level community detection without predetermined tags. It aims to obtain fuzzy topic features of the community and finalize the community alignment across social networks. Furthermore, iterative alignment is executed from coarse-grained communities to fine-grained sub-communities until user-level alignment occurs. The process can be terminated at any layer to achieve multi-granularity alignment, which resolves the low accuracy issue of edge user alignment at a single granularity and improves the accuracy of user alignment. The effectiveness of the proposed method is shown by implementing real datasets.