Large language models (LLMs) increasingly rely on external knowledge to improve factuality, yet many real-world knowledge sources are organized as heterogeneous graphs rather than plain text. Reasoning over such graphs requires models to follow schema-defined relations through precise function calls and to aggregate evidence across multiple rounds of interaction. We propose GraphDancer, a two-stage post-training framework that teaches LLMs to reason over graphs by interleaving natural-language reasoning with graph function execution. The first stage teaches the model how to interact with the graph under rule-based rewards, while the second stage further teaches it to prefer more grounded and efficient interaction trajectories. The key novelty of GraphDancer is a graph-aware curriculum that organizes both stages by the structural complexity of information-seeking trajectories, progressively increasing task difficulty during training. We evaluate GraphDancer on a multi-domain benchmark by training on one domain only and testing on unseen domains and out-of-distribution question types. Despite using only a 3B backbone, GraphDancer outperforms baselines equipped with larger/stronger backbones, demonstrating robust cross-domain generalization of graph exploration and reasoning skills. Our code can be found at https://github.com/leopoldwhite/GraphDancer.