Being the largest blockchain with the capability of running smart contracts, Ethereum has attracted wide attention and its market capitalization has reached 20 billion USD. Ethereum not only supports its cryptocurrency named Ether but also provides a decentralized platform to execute smart contracts in the Ethereum virtual machine. Although Ether's price is approaching 200 USD and nearly 600K smart contracts have been deployed to Ethereum, little is known about the characteristics of its users, smart contracts, and the relationships among them. To fill in the gap, in this paper, we conduct the first systematic study on Ethereum by leveraging graph analysis to characterize three major activities on Ethereum, namely money transfer, smart contract creation, and smart contract invocation. We design a new approach to collect all transaction data, construct three graphs from the data to characterize major activities, and discover new observations and insights from these graphs. Moreover, we propose new approaches based on cross-graph analysis to address two security issues in Ethereum. The evaluation through real cases demonstrates the effectiveness of our new approaches.