The purpose of our study is to figure out the transitions of the cryptocurrency market due to the outbreak of COVID-19 through network analysis, and we studied the complexity of the market from different perspectives. To construct a cryptocurrency network, we first apply a mutual information method to the daily log return values of 102 digital currencies from January 1, 2019, to December 31, 2020, and also apply a correlation coefficient method for comparison. Based on these two methods, we construct networks by applying the minimum spanning tree and the planar maximally filtered graph. Furthermore, we study the statistical and topological properties of these networks. Numerical results demonstrate that the degree distribution follows the power-law and the graphs after the COVID-19 outbreak have noticeable differences in network measurements compared to before. Moreover, the results of graphs constructed by each method are different in topological and statistical properties and the network's behavior. In particular, during the post-COVID-19 period, it can be seen that Ethereum and Qtum are the most influential cryptocurrencies in both methods. Our results provide insight and expectations for investors in terms of sharing information about cryptocurrencies amid the uncertainty posed by the COVID-19 pandemic.
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