Much of the current research in Ethereum transaction records focuses on the statistical analysis and measurements of existing data; however, the evolution mechanism of Ethereum transactions is an important, yet seldom discussed issue. In this work, we first collect the transaction data of Ethereum and build network models from a microlevel view and then use a link-prediction-based framework to quantify the impact of network characteristics on Ethereum evolution. Next, we explore the graph structure properties and the driving factors of newly generated transaction relationships. Experimental results show that the local and microscopic structure of Ethereum networks is star-shaped, and the transaction frequency of addresses has a great impact on the evolution of Ethereum transaction relationships. First-layer nodes of microstructures dominate the network evolution. Moreover, the degree of addresses is an effective basis for predicting the direction of new transactions. Potential further studies on Ethereum transaction link prediction are discussed, for example, the label effect of center addresses.