Data-centric AI, with its primary focus on the collection, management, and utilization of data to drive AI models and applications, has attracted increasing attention in recent years. In this article, we conduct an in-depth and comprehensive review, offering a forward-looking outlook on the current efforts in data-centric AI pertaining to graph data-the fundamental data structure for representing and capturing intricate dependencies among massive and diverse real-life entities. We introduce a systematic framework, Data-centric Graph Machine Learning (DC-GML), that encompasses all stages of the graph data lifecycle, including graph data collection, exploration, improvement, exploitation, and maintenance. A thorough taxonomy of each stage is presented to answer three critical graph-centric questions: (1) how to enhance graph data availability and quality; (2) how to learn from graph data with limited-availability and low-quality; (3) how to build graph MLOps systems from the graph data-centric view. Lastly, we pinpoint the future prospects of the DC-GML domain, providing insights to navigate its advancements and applications.