Recent years have witnessed significant advancements in graph machine learning (GML), with its applications spanning numerous domains. However, the focus of GML has predominantly been on developing powerful models, often overlooking a crucial initial step: constructing suitable graphs from common data formats, such as tabular data. This construction process is fundamental to applying graph-based models, yet it remains largely understudied and lacks formalization. Our research aims to address this gap by formalizing the graph construction problem and proposing an effective solution. We identify two critical challenges to achieve this goal: 1. The absence of dedicated datasets to formalize and evaluate the effectiveness of graph construction methods, and 2. Existing automatic construction methods can only be applied to some specific cases, while tedious human engineering is required to generate high-quality graphs. To tackle these challenges, we present a two-fold contribution. First, we introduce a set of datasets to formalize and evaluate graph construction methods. Second, we propose an LLM-based solution, AutoG, automatically generating high-quality graph schemas without human intervention. The experimental results demonstrate that the quality of constructed graphs is critical to downstream task performance, and AutoG can generate high-quality graphs that rival those produced by human experts. Our code can be accessible from https://github.com/amazon-science/Automatic-Table-to-Graph-Generation.