Large-scale graph data in the real-world are often dynamic rather than static. The data are changing with new nodes, edges, and even classes appearing over time, such as in citation networks and research-and-development collaboration networks. Graph neural networks (GNNs) have emerged as the standard method for numerous tasks on graph-structured data. In this work, we employ a two-step procedure to explore how GNNs can be incrementally adapted to new unseen graph data. First, we analyze the verge between transductive and inductive learning on standard benchmark datasets. After inductive pretraining, we add unlabeled data to the graph and show that the models are stable. Then, we explore the case of continually adding more and more labeled data, while considering cases, where not all past instances are annotated with class labels. Furthermore, we introduce new classes while the graph evolves and explore methods that automatically detect instances from previously unseen classes. In order to deal with evolving graphs in a principled way, we propose a lifelong learning framework for graph data along with an evaluation protocol. In this framework, we evaluate representative GNN architectures. We observe that implicit knowledge within model parameters becomes more important when explicit knowledge, i.e., data from past tasks, is limited. We find that in open-world node classification, the data from surprisingly few past tasks are sufficient to reach the performance reached by remembering data from all past tasks. In the challenging task of unseen class detection, we find that using a weighted cross-entropy loss is important for stabilit
