•From the network science perspective, the Ethereum transactional behaviors such as the transaction volume, the transaction relation and the component structure of the graph share a similarity in that they exhibit the heavy-tail properties and could be approximated statistically by the power law function.•This research is the first work that provides a relatively comprehensive investigation into the transaction data recorded in the Ethereum blockchain and tries to find the statistical laws of the data from the perspective of network science.•Experiments also indicate that the transaction network exhibits a bow-tie structure with negative assortativity if it is seen as a directed network. In recent years, the rapid development of blockchain technologies has attracted considerable attention. However, little effort has been devoted toward investigating the large amount of trade data recorded in blockchains. This paper focuses on transaction data in Ethereum, which is a prominent public blockchain platform supporting not only secure cryptocurrency transfer but also various decentralized applications. By means of the framework of network science theory, we find that several transaction features, such as transaction volume, transaction relation, and component structure, exhibit a heavy-tailed property and can be approximated by the power law function. In particular, we find that the transaction relations follow a bow-tie structure with negative assortativity if they are regarded as a directed graph. The popular hubs tend to connect to a large number of common users. We believe that the aforementioned statistics can be ascribed to the vast diversity of transactions and the existence of a number of cryptocurrency exchanges. To the best of our knowledge, this study is the first to not only carry out a relatively comprehensive investigation of the transaction data recorded in Ethereum but also probe the statistical laws underlying the transaction relationships from the perspective of network science.