By analyzing the foreign exchange market data of various currencies, we investigate the topology of correlation networks among 45 major currencies using the minimal spanning tree (MST) and the planar maximally filtered graph (PMFG). Besides the geographical location, our paper uses interest rates as another labeling criterion to analyze the currency network. Some conclusions are given: the mean values of the correlation coefficients dropped dramatically in economic crisis, such as September 2008 and March 2020. Also, the overall correlation between currencies has gradually weakened in recent years; When interest rate is used as the labeling criteria, the currencies of countries with low interest rates are mostly surrounded by the EUR; The PMFG method contains more links that are filtered in the MST and displays different results on degree centrality analysis, providing complementary information for the MST result; the Commonwealth cluster is also found. Our findings can help to discover the economic cycles and market crashes by studying topological and statistical properties of the currency network. •Our study focuses on two financial crises, especially during the Covid-19 pandemic.•MST and PMFG are used to study the topological structures of the FX market.•The PMFG method can provide complementary information for MST.•Another labeling criterion, interest rate, is introduced to analyze the result.•The robustness check in the study of complex networks is also performed.