[Objective] This paper systematically reviews the progress and trends of graph database research and applications for complex network analysis. [Coverage] We searched the Web of Science, Scopus, and CNKI database for Chinese and English literature. A total of 15 graph databases and open-source packages, 21 practical cases, and 14 research papers were retrieved. [Methods] First, we compared the mainstream graph database products from China and abroad. Then, we explored the latest solutions for complex network analysis, including algorithms (such as centrality, path finding, link prediction, and community detection), graph visualization, performance and related applications. [Results] The graph database has become an important analysis tool and research method for complex network analysis and big data mining. They also work closely with graph computing engines for complex network analysis. [Limitations] This paper only examined a few representative cases. [Conclusions] The graph database could effectively query, represent and analyze complex network data for their patterns or structures. Their presentation of multi-dimensional data is crucial for mining implicit relationships. © 2022, Chinese Academy of Sciences. All rights reserved.