We present a novel real-time line segment detection scheme called Line Graph Neural Network (LGNN). Existing approaches require a computationally expensive verification or postprocessing step. Our LGNN employs a deep convolutional neural network (DCNN) for proposing line segment directly, with a graph neural network (GNN) module for reasoning their connectivities. Specifically, LGNN exploits a new quadruplet representation for each segment where the GNN module takes the predicted candidates as vertexes and constructs a sparse graph to enforce structural context. Compared with the state-of-the-art, LGNN achieves near real-time performance without compromising accuracy. LGNN further enables time-sensitive 3D applications. When a 3D point cloud is accessible, we present a multi-modal line segment classification technique for extracting a 3D wireframe of the environment robustly and efficiently.