This paper tackles a 2D architecture vectorization problem, whose task is to infer an outdoor building architecture as a 2D planar graph from a single RGB image. We provide a new benchmark with ground-truth annotations for 2,001 complex buildings across the cities of Atlanta, Paris, and Las Vegas. We also propose a novel algorithm utilizing 1) convolutional neural networks (CNNs) that detects geometric primitives and infers their relationships and 2) an integer programming (IP) that assembles the information into a 2D planar graph. While being a trivial task for human vision, the inference of a graph structure with an arbitrary topology is still an open problem for computer vision. Qualitative and quantitative evaluations demonstrate that our algorithm makes significant improvements over the current state-of-the-art, towards an intelligent system at the level of human perception. We will share code and data.