Graph data, such as scene graphs and knowledge graphs, see wide use in AI systems. In real-world and large applications graph data are usually incomplete, motivating graph reasoning models for missing-fact or missing-relationship inference. While these models can achieve state-of-the-art performance, they require a large amount of training data.Recent years have witnessed the rising interest in label creation with data programming (DP) methods, which aim to generate training labels from heuristic labeling functions. However, existing methods typically focus on unstructured data and are not optimized for graphs. In this work, we propose LogicDP, a data programming framework for graph data. Unlike existing DP methods, (1) LogicDP utilizes the inductive logic programming (ILP) technique and automatically discovers the labeling functions from the graph data; (2) LogicDP employs a budget-aware framework to iteratively refine the functions by querying an oracle, which significantly reduces the human efforts in function creations. Experiments show that LogicDP achieves better data efficiency in both scene graph and knowledge graph reasoning tasks.