Data selection methods, such as active learning and core-set selection, are useful tools for improving the data efficiency of deep learning models on large-scale datasets. However, recent deep learning models have moved forward from independent and identically distributed data to graph-structured data, such as social networks, ecommerce user-item graphs, and knowledge graphs. This evolution has led to the emergence of Graph Neural Networks (GNNs) that go beyond the models existing data selection methods are designed for. Therefore, we present Grain, an efficient framework that opens up a new perspective through connecting data selection in GNNs with social influence maximization. By exploiting the common patterns of GNNs, Grain introduces a novel feature propagation concept, a diversified influence maximization objective with novel influence and diversity functions, and a greedy algorithm with an approximation guarantee into a unified framework. Empirical studies on public datasets demonstrate that Grain significantly improves both the performance and efficiency of data selection (including active learning and core-set selection) for GNNs. To the best of our knowledge, this is the first attempt to bridge two largely parallel threads of research, data selection, and social influence maximization, in the setting of GNNs, paving new ways for improving data efficiency.