In this paper, we present a novel framework to detect line segments in man-made environments. Specifically, we propose to describe junctions, line segments and relationships between them with a simple graph, which is more structured and informative than end-point representation used in existing line segment detection methods. In order to extract a line segment graph from an image, we further introduce the PPGNet, a convolutional neural network that directly infers a graph from an image. We evaluate our method on published benchmarks including York Urban and Wireframe datasets. The results demonstrate that our method achieves satisfactory performance and generalizes well on all the benchmarks. The source code of our work is available at https://github.com/svip-lab/PPGNet.