Intrinsically motivated exploration has proven useful for reinforcement learning, even without additional extrinsic rewards. When the environment is naturally represented as a graph, how to guide exploration best remains an open question. In this work, we propose a novel approach for exploring graph-structured data motivated by two theories of human curiosity: the information gap theory and the compression progress theory. The theories view curiosity as an intrinsic motivation to optimize for topological features of subgraphs induced by nodes visited in the environment. We use these proposed features as rewards for graph neural-network-based reinforcement learning. On multiple classes of synthetically generated graphs, we find that trained agents generalize to longer exploratory walks and larger environments than are seen during training. Our method computes more efficiently than the greedy evaluation of the relevant topological properties. The proposed intrinsic motivations bear particular relevance for recommender systems. We demonstrate that next-node recommendations considering curiosity are more predictive of human choices than PageRank centrality in several real-world graph environments.